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10R Unit 8 Similarity CW 8.1 HW: Worksheet #8.1 (following these notes) Relationships of Side Lengths and Angle Measures Theorem: ________________________________________________________________________ Practice: _______________1. State the longest side of the triangle. Justify your answer. _______________2. The ratio of : : 8 : 7 :3A B C∠ ∠ ∠ = . State the longest side of the triangle. Justify your answer.   _______________3. State the longest side of the triangle. Justify your answer. _______________4. State the smallest angle of the triangle. Justify your answer. _______________5. Express the relationship of the angles of the triangle as an inequality in order from smallest to largest.

 

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_______________6. State the longest side of the triangle. Justify your answer. _______________7. In triangle PQR, : : 3: 2 :1P Q R∠ ∠ ∠ = . State the shortest side of the triangle and justify your answer. _______________8. In right triangle ABC, BC is the hypotenuse, 9AB = , and 12AC = . State the smallest angle of the triangle and justify your answer. _______________9. In right triangle PQR, PR is the hypotenuse, 24QR = , and 25PR = . State the smallest angle of the triangle and justify your answer. _______________10. In ABCΔ , side AC is extended through point D such that BCD∠ is an exterior

angle. If 13m A x∠ = , 10m B∠ = , and 136m BCD x∠ = − + . State the longest side of the triangle and justify your answer.

_______________11. The ratio of the lengths of the sides of ABCΔ is : : 4 : 5 : 6AB BC CA = . If the perimeter of the triangle is 75, state the largest angle of the triangle and justify your answer.

 

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10R Unit 8 Similarity HW 8.1 Relationships of Side Lengths and Angle Measures 1. Using the graph below, express the angles of the triangle as an inequality from least to greatest. HINT: You MUST use the distance formula three times. _______________2. Express the relationship of the angles of the triangle as an inequality in order from smallest to largest. _______________3. The perimeter of ABCΔ is 78. Use the diagram to the right to determine the smallest angle of the triangle and justify your answer. _______________4. In obtuse ABCΔ with obtuse C∠ , side AC is extended through point D such that BCD∠ is an acute exterior angle. If 5 2m A x∠ = + , 3 4m B x∠ = − , and 12m BCD x∠ = + . State the shortest side of the triangle and justify your answer.

 

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10R Unit 8 Similarity CW 8.2 HW: Worksheet #8.2 (following these notes) Introduction to Similar Figures & Geometric Mean

Warm-up: Factor: 2 15 26x x− + FOIL to check your answer: What is a ratio? _____________________________________________________________________ Expressed 3 Ways: a.)__________ b.)__________ c.)__________ “The product of the __________ equals the product of the __________.” This is the new and improved way of saying: ________ ____________. Solving Proportions: Solve for the value(s) of x. Use ( ), you may have to distribute or FOIL. 1. a) 3 2

5 1m m=

+ + b) 8 2

2 4z

z+=

−

2. In the diagram at the right, ab= 34

. Complete each statement.    

a) ba= b) 4a = c) b

4= d) 7

4=

Symbol for Similar: ________ Extended Proportions: Used to write a similarity statement.

 

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3. Given that ΔMNP ~ ΔSRT, state the corresponding angles that are congruent and write a similarity statement. ∠M ≅ ∠ ____ ∠N ≅ ∠ ____ ∠P ≅ ∠ ____ Similarity Statement: ______ = ______ = _______ Scale Factor: Think “Dilation” ____________________________________________________________ 4. Using the diagram to the right: ___________ a) What type of triangle is illustrated? Explain. ___________ b) Find the scale factor of (image) ABCΔ to (pre-image) DEFΔ . This is also known as the ratio of sides. ___________ c) What is the ratio of the perimeters? ___________ d) What is the ratio of areas?

Basic Similarity Word Problems: __________5. Triangles ABC and HIJ are similar. The length of the sides of ABC are 102, 162, and 96. The length of the smallest side of HIJ is 32, what is the length of the longest side of HIJ? __________6. Triangles HIJ and MNO are similar. The perimeter of smaller triangle HIJ is 44. The lengths of two corresponding sides on the triangles are 13 and 26. What is the perimeter of MNO? __________7. Triangles GHI and MNO are similar. GI:MO = 4:3, and MN = 87, what is the length of GH?

If the ratio of sides is a:b, then the ratio of perimeters is ___:___ and the ratio of areas is ___:___.

 

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__________8. A tree 42 feet tall casts a shadow 120 feet long. Paul is 3 1/2 feet tall. How long is Paul's shadow? __________9. Triangles KLM and STU are similar. The length of the sides of KLM are x + 82, 4x - 26, and 5x - 90. The perimeter of KLM is 306. The perimeter of STU is 459, what is the length of the longest side of STU?

Mean Proportional: is also known as the Geometric Mean To find the mean proportional between two given numbers: a.) _________________________________ b.) _________________________________ c.) _________________________________ Practice: Find the geometric mean of the two given numbers in simplest radical form. __________10. 2 and 8 __________11. 3 and 9 __________12. 7 and 14 __________13. 8 and 16

 

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10R Unit 8 Similarity HW 8.2 Introduction to Similar Figures & Geometric Mean 1. Given that ABCD ~ EFGD: a) ∠A ≅ _____ ∠C ≅ _____ ∠F ≅ _____ b) Write a similarity statement: _____ = _____ = _____ = _____ c) What is the scale factor of ABCD to EFGD? _________ d) Is this “dilation” an enlargement or a reduction? _______________ e) What is the value of x? _______ What is the value of y? _______ 2. Find the geometric mean of the two given numbers in simplest radical form. __________a.) 10 and 12 __________b.) 9 and 13 3. Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain. a) b) 4. A company produces a standard-size U.S. flag that is 3 ft. by 5 ft. The company also produces a giant- size flag that is similar to the standard-size flag. If the shorter side of the giant-size flag is 36ft, what is the length of its longer side? 5. Two polygons have corresponding side lengths that are proportional. Can you conclude that the polygons are similar? Justify your answer. 6. A cartographer is making a map of Pennsylvania. She uses the scale 1 in = 10 mi. The actual distance between Harrisburg and Philadelphia is about 95 mi. How far apart should she place the two cities on the map? 7. In the diagram to the right, ΔDFG ~ ΔHKM. Find each of the following. a) The scale factor of ΔHKM to ΔDFG. _______ b) m∠K _______ c) MK _______

 

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10R Unit 8 Similarity CW 8.3 HW: Worksheet #8.3 (following these notes) Similarity Theorems

Warm-up: Simplify: 299x y 396x 10150a Theorem: _____________________________________________________________________ _____________________________________________________________________ Two Methods: *Depends on the picture you are given!

1. “Top of the Mountain” a a cb d

+= 2. “Side to Side” a ca b c d

=+ +

a cb d=

Use when you have the bottom of the mountain. Use when you have the sides of the mountain. Practice: Solve for x. __________1. __________2. __________3. __________4. __________5. Simplest radical form. __________6. Simplest radical form.

 

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7. Determine whether ||PS QR . 8. Is ||BD CE ? __________9. In the diagram below, ||AB CD . Find the value of AC . __________10.In ABCΔ , point D lies on AB and point E lies on BC such that ||DE AC . If AD x= , 4DB = , DE x= , and 8AC = , find AB . __________11. In PQRΔ , point S lies on QR and point T lies on PR such that ||ST PQ . If 3RS = , 20PT = , 2RT x= , 5QS = , find PR in simplest radical form.

__________12. For each part, you are given AB AEBC ED

= . Find BC .

__________ a.) b.)

What is another name for , in this case?

_____________ _____________

 

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10R Unit 8 Similarity HW 8.3 Similarity Theorems Find each variable: ______1) ______2) ______3) ______4) ______5) ______6) ______7) ______8) ______9) In VLMN , point O lies on LM and point P lies on NM such that LN POP . If LO = 10 , OM = x , NM = 45 , and PN = 30 , find OM . ______10) In , point D lies on and point E lies on such that . If AD = 12 , DB = 9 , BE = x + 4 and EC = 2x , find BC .

ABCΔ AB BC ||DE AC

 

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10R Unit 8 Similarity CW 8.4 HW: Worksheet #8.4 (following these notes) Similarity Theorems - Practice

Warm-up: Solve for the value(s) of x: 2 22 50 3 4x x x− = + + Theorem: If a line parallel to one side of a triangle intersects the other two sides, then

it divides the two sides proportionally (& vice versa). More Practice: __________1. __________2. __________3. __________4.

__________5. __________6. Given AB FEBC ED

= . Find AC .

 

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Two Other Similarity Theorems: If three parallel lines intersect two transversals, then they divide the transversals proportionally.

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

__________7. Given || ||a b c , solve for x. __________8. Find the length of AB . __________9. 41st Street, 42nd Street and 43rd Street __________10. ADbisects CAB∠ , find AC . all lie parallel. Find the distance between 42nd and 43rd running along Broadway. __________11. Find the length of AB . __________12. Solve for x.

 

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10R Unit 8 Similarity HW 8.4 Similarity Theorems - Practice _________1. The ratio of the perimeters of two similar figures is 5 : 9. What is the ratio of the areas? _________2. Using the extended ratios indicated in the drawing to the right, _________ an artist can sketch the proper placement of the eyes, nose and _________ mouth of an adult or infant’s face. _________ a) If AE = 72 cm in the diagram, find AB, BC, CD and DE. _________ b) If PT = 21 inches, how far from the top should you place the line for the eyes? _________3. Three campsites are shown in the diagram to the right. What is the length of Site A along the river? 4. Solve for x. ______a) _______b) ______c) ______d)

 

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_______e) _____f) 5. Solve for x. _____a) ______b) 6. In Washington DC, E. Capitol Street, Independence Avenue, C Street and D Street are parallel streets that intersect Kentucky Avenue and 12th Street. ______a) How long (to the nearest foot) is Kentucky Avenue

between C Street and D Street?

______a) How long (to the nearest foot) is Kentucky Avenue between E. Capitol Street and Independence Avenue?

 

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10R Unit 8 Similarity CW 8.5 HW: Finish this CW 8.5 Similarity Review Answers & Work = Consult Teacher Website Similarity Theorems: THEOREM: DIAGRAM:

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

If three parallel lines intersect two transversals, then they divide the transversals proportionally.

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

Can prove triangles similar by:

AA – need 2 angles in each triangle (most common) SAS – need 1 angle in each and verify 1 proportion SSS – verify 2 proportions

 

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__________1. A triangle has sides whose lengths are 5, 12, and 13. A similar triangle could have sides with lengths of (1) 3, 4, and 5 (3) 7, 24, and 25 (2) 6, 8, and 10 (4) 10, 24, and 26

__________2. The accompanying diagram shows two similar triangles. Which proportion could be used to solve for x?

(1) 9

24 15x = (2)

32 1215x

=

(3) 24 159 x

= (4) 32 1512 x

=

__________3. __________4. In  the  accompanying  diagram,  ΔQRS  is  similar  to  ΔLMN ,  

RQ = 30,  QS = 21,   SR = 27,  and   LN = 7.    What  is  the    length  of   ML ?  

__________5. In  the  accompanying  diagram,  triangle  A  is  similar    

 to  triangle  B.    Find  the  value  of  n.   __________6. The  Rivera  family  bought  a  new  tent  for  camping.  Their  old  tent    

 had  equal  sides  of  10  feet  and  a  floor  width  of  15  feet,  as  shown      in  the  accompanying  diagram.  

If  the  new  tent  is  similar  in  shape  to  the  old  tent  and  has  equal    

 sides  of  16  feet,  how  wide  is  the  floor  of  the  new  tent?  

 

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__________7. In obtuse PQRΔ with obtuse Q∠ , side RQ is extended through point S such that PQS∠ is an acute exterior angle. If 6 3m P x∠ = + , 2 6m R x∠ = + , and 10 5m SQP x∠ = − , state the shortest side of the triangle and justify your answer. __________8. Triangle RST has a perimeter of 92. If 5 1RS x= + , 3 5ST x= + , and 3 2RT x= − , which of the following is true?

(1) S T∠ >∠ (2) S R∠ >∠ (3) T S∠ >∠ (4) T R∠ =∠

__________9. Fran’s favorite photograph has a length of 6 inches and a width of 4 inches.

She wants to have it made into a poster with dimensions that are similar to those of the photograph. She determined that the poster should have a length of 24 inches. How many inches wide will the poster be?

__________10. Fran has another photograph that has a length of 5 inches. She had it __________ increased by a scale factor of 4, so the ratio between them is 5:20 or 1:4. __________ What is the ratio of the altitudes of the photos? What  is  the  ratio  of    

     the  perimeters?    What  is  ratio  of  the  areas?  

__________11. Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller  sail?

(1) 15 ft (2) 60 ft (3) 36 ft (4) 100 ft

 

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__________12. Two triangles are similar. The lengths of the sides of the smaller

triangle are 3, 5, and 6, and the length of the longest side of the larger triangle is 18. What is the perimeter of the larger triangle?

(1) 14 (2) 24 (3) 18 (4) 42

__________13. The base of an isosceles triangle is 5 and its perimeter is 11. The

base of a similar isosceles triangle is 10. What is the perimeter of the larger triangle?

(1) 15 (2) 22 (3) 21 (4) 110

__________14. Pentagon ABCDE is similar to pentagon FGHIJ. The lengths of the

sides of ABCDE are 8, 9, 10, 11, and 12. If the length of the longest side of pentagon FGHIJ is 18, what is the perimeter of pentagon FGHIJ?

(1) 50 (2) 75 (3) 56 (4) 100

__________15.    Which  is  not  a  property  of  all  similar  triangles?    

   (1)  The  corresponding  angles  are  congruent.      (2)  The  corresponding  sides  are  congruent.      (3)  The  perimeters  are  in  the  same  ratio  as  the  corresponding  sides.      (4)  The  altitudes  are  in  the  same  ratio  as  the  corresponding  sides.  

__________16.  Two  triangles  are  similar,  and  the  ratio  of  each  pair  of    

   corresponding  sides  is  2:1.  Which  statement  regarding  the        two  triangles  is  not  true?  

     (1)  Their  areas  have  a  ratio  of  4  :  1.      (2)  Their  altitudes  have  a  ratio  of  2  :  1.      (3)  Their  perimeters  have  a  ratio  of  2  :  1.      (4)  Their  corresponding  angles  have  a  ratio  of  2  :  1.  

__________17. __________18.To the nearest tenth,            

 

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 __________19. In the diagram to the right, lines a, b, and c are cut

by transversals d and e such that || ||a b c . Solve for x.

__________20. In the diagram to the right, ADbisects BAC∠ . Solve for the value of x.         Review Questions to Study: __________21. In triangle ABC, AF FC≅ , BD AC⊥ , and

BEbisects ABC∠ . Which of the following is false? (1) ABE CBE∠ ≅ ∠ (2) BD is the altitude to AC (3) ABD CBD∠ ≅ ∠ (4) BF is the median to AC

__________22. Which of the following is the correct equation of the circle in the graph to the right?

(1) ( ) ( )2 22 1 3x y− + + =

(2) ( ) ( )2 22 1 9x y− + + =

(3) ( ) ( )2 22 1 3x y+ + − =

(4) ( ) ( )2 22 1 9x y+ + − = 23a) Complete the following logic rules: Conjunction Disjunction Conditional Bi-Conditional

p   q   p∨q  T   T      T   F      F   T      F   F    

b) Write the justification used for each truth table. A conjunction is only _____________________ A conditional is only ________________________

p   q   p∧q  T   T      T   F      F   T      F   F      

 

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A disjunction is only ______________________ A bi-conditional is only ______________________ Sketch a diagram for each of the following: __________24. Two planes perpendicular to the same line are (1) intersecting (2) perpendicular (3) skew (4) parallel __________25. If two different lines are perpendicular to the same plane, they are (1) coplanar (2) consecutive (3) collinear (4) congruent __________26. If a line is perpendicular to a plane, then any line perpendicular to the

given line at its point of intersection with the given plane (1) is parallel to the given plane (2) is perpendicular to the given plane (3) lies in the given plane (4) is parallel to the given line 27. When do you use the distance formula? _______________ Keywords: ________________________ When do you use the midpoint formula? ______________ Keywords: ________________________ When do you use the slope formula? _______________ Keywords: ________________________ 28. a) Graph and label triangle ABC with ( )1,6A , ( )2,1B , ( )7,2C . b) Show ABCΔ is an isosceles triangle. c) Find the coordinates of D, the point that bisects AC . d) Show AC BD⊥

 

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10R Unit 8 Similarity CW 8.6 HW: Worksheet #8.6 (following these notes) Similarity Proofs by Angle-Angle (AA~thm) Warm-up: Write the equation of the line parallel to the line 4 28y x+ = through the point (-2, 10). To Prove Triangles are Similar: _________________________________________________________ Symbol for Similar: _________

1. Given: ||DE AC Prove: a.) ~DBE ABCΔ Δ

b.) DB DEAB AC

=

c.) DB AC AB DE• = •      

2. Given: ||AB DE Prove: a.) ~ABC EDCΔ Δ

b.) AC ABEC ED

=

c.) AC ED EC AB• = •  

Statement Reason 1. ||DE AC

2. BDE BAC∠ ≅ ∠

3. B B∠ ≅ ∠

4. ~DBE ABCΔ Δ

5. DB DEAB AC

=

6. DB AC AB DE• = •

Statement Reason 1. ||AB DE

2. ACB ECD∠ ≅ ∠

3. B D∠ ≅ ∠

4. ~ABC EDCΔ Δ

5. AC ABEC ED

=

6. AC ED EC AB• = •

 

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What did the first two examples had in common, besides starting with “Given”? __________________________________________________  __________________________________________________  __________________________________________________    3. Given: PS ST⊥ , PQ QR⊥ Prove: PS PR PQ PT• = • 4. Given: PQR TSR∠ ≅ ∠ , PR QS⊥ Prove: ~PQR TSRΔ Δ 5. Given: BA is the altitude to AC ED is the altitude to DF 3 4∠ ≅ ∠

Prove: AB BCED EF

=

 

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10R Unit 8 Similarity HW 8.6 Similarity Proofs by Angle-Angle (AA~thm) Complete the following. Proofs are nothing more than time and effort. 1. Given: ||BE CD Prove: AB CD AC BE• = •   2. Given: ||PQ TS Prove: ~PQR TSRΔ Δ 3. Given: LM is the altitude to MP LN is the altitude to NO Prove: LM NO MP LN• = •

Statement Reason 1. ||BE CD

2. ABE ACD∠ ≅ ∠

3. A A∠ ≅ ∠

4. ~ABE ACDΔ Δ

5. AB BEAC CD

=

6. AB CD AC BE• = •

 

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10R Unit 8 Similarity CW 8.7 HW: Worksheet #8.7 (following these notes) Similarity Proofs by SAS~thm & SSS~thm Warm-up: Q is the incenter of ABCΔ . If 50QC = , 48FC = , and 7EQ x= , solve for the value of x. In addition to proving triangles similar by ______, you can also prove them similar by _______ & _______. _______ is the most common. To prove by _______, you need to verify _______ proportion and have one pair of _______ angles. To prove by _______, you need to verify _______ proportions. Practice: Determine whether the following can be proven similar using the AA, SAS, SSS ~thm. 1. 2. 3. 4. 5. 6.

 

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Extra Practice: 7. Given: QRSΔ is isosceles with vertex R∠ QTU QRS∠ ≅ ∠ Prove: QT RS QR TU• = • 8. Given: CA is the altitude to AB CDis the altitude to DE Prove: ~ABC DECΔ Δ 9. Given: ||AB DE Prove: AB EC DE BC• = •

 

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Optional: SAS and SSS Proofs

10. Given: CD CECA CB

=

Prove: ~CDE CABΔ Δ

11. Given: AB BCDE EF

= , AC BCDF EF

=

Prove: ~ABC DEFΔ Δ

12. Given: AC BCDC EC

=

Prove: ~ABC DECΔ Δ

 

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10R Unit 8 Similarity HW 8.7 Similarity Proofs by SAS~thm & SSS~thm Remember: Corresponding __________ of __________ triangles are _____ _______________. And: The product of the __________ equals the __________ of the __________. How many proportions do you need to verify for SAS~thm?_____ How many proportions do you need to verify for SSS~thm? _____ How many proportions do you need to verify for AA~thm? _____ Practice: Determine whether the following can be proven similar using AA, SAS, SSS. 1. 2. 3. 4. 5. 6. 7. 8.

 

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9. Given triangle ABC with ( )1,1A , ( )4,1B , ( )1,5C and

triangle DEF with ( 2, 2)D − − , ( )8, 2E − − , ( )2, 10F − − , prove that ~ABC DEFΔ Δ .

__________What is the ratio of the perimeters of ABC to DEF? __________What is the ratio of the areas of ABC to DEF? 10. Given: ||AD CB Prove: CB DE DA CE• = • 11. Given: AE EF⊥ , AB BC⊥ Prove: a.) ~AEF ABCΔ Δ

b.) AE EFAB BC

=

c.) AB EF AE BC• = •

 

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10R Unit 8 Similarity CW 8.8 HW: Finish this Review Packet! Review Packet Answers = Consult Teacher Website Similarity Theorems: THEOREM: DIAGRAM:

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

If three parallel lines intersect two transversals, then they divide the transversals proportionally.

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.

Can prove triangles similar by:

AA – need 2 angles in each triangle (most common) SAS – need 1 angle in each and verify 1 proportion SSS – verify 2 proportions

 

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Practice: __________1. In the accompanying diagram of ∆ABC, ||DE AB ,

9CA = , 3DA = , and 10CE = . Find EB . __________2. Triangle ABC is similar to triangle DEF. If 6AB = , 7BC = , 12DE = , and 10DF = , find

the perimeter of DEFΔ and state the scale factor. __________3. Triangle ABC is similar to triangle DEF. If 4AB = , 6BC = , 6DE = , and 12DF = , find

the perimeter of DEFΔ and state the scale factor. __________4. Given PQRΔ , S lies on PQand T lies on QR such that ||ST PR but ST is NOT a

midsegment of PQRΔ , find the measure of ST if 6PS = , 3SQ = , and 15PR = . __________5. For each of the following, find the length of AB . __________ __________ __________6. The perimeter of a rectangular garden is 220 meters. The ratio of its length to width is 8 : 3. What is the length of the field?

 

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__________7. Find the length of BC . 8. Verify that ~ABC DEFΔ Δ for the given information below: : 6, 9, 12ABC AC AB BCΔ = = = : 2, 3, 4DEF DF DE EFΔ = = = How many proportions must be verified for SSS similarity? _____ For SAS? _____ __________9. Triangles BCD and UVW are similar where BCD is the smaller triangle. The lengths of two corresponding sides on the triangles are 31 and 186. One side of UVW is 192. What is the length of the corresponding side on BCD? __________10. Show that the triangles below are similar and write a similarity statement and state the scale factor. __________ __________11. Triangles CDE and IJK are similar. CE:IK = 2:6, and JK = 78, what is the length of DE? __________12. Is ~AEB ADCΔ Δ ? If so, by what theorem? __________13. If the ratio of the perimeters of two similar triangles is 4:5, what is the ratio of their areas? __________14. If the ratio of the perimeters of two similar triangles is 8:3, what is the ratio of their areas?

 

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15. Determine whether the triangles are similar. If so, write a similarity statement and the postulate or theorem that justifies your answer. a.) b.) c.) __________16. The measures of the angles of a triangle are in the extended ratio 2:3:5. Find the measures of the angles. __________17. A tree casts a shadow that is 30 feet long. At the same time, a person standing nearby who is five feet two inches tall casts a shadow that is 50 inches long. How tall is the tree, to the nearest foot? **Watch the units! __________18. The length of a rectangle is 20 meters and the width is 15 meters. Find the ratio of width to length of the rectangle. Then, simplify the ratio. 19. Find the geometric mean of each of the following in simplest radical form. __________a.) 8 and 12 __________b.) 3 and 15 __________c.) 7 and 14 __________d.) 3 and 26

__________20. In the diagram, BA BCDA EC

= . Find BD .

 

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__________21. If 1AD = , BD x= , AE x= , and 2EC x= + . Find DB . __________22. If AD x= , 5ED = , 2DB = , and 2BC x= + . Find AD .  __________23. Find the length of WT . __________24. Two similar posters have a scale factor of 4:5. The large poster’s perimeter is 85 inches. Find the small poster’s perimeter. 25. Determine whether the polygons are similar. If so, write a similarity statement and find the scale factor. a.) b.)

__________26.The slope of a ramp is 35

. If the rise of a similar ramp is 18, what is its run?

 

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27. Use the given information to determine whether ||AB CD . a.) b.) 28. Determine whether the following can be proven similar using AA, SAS, SSS. a.) b.) c.) d.) __________29. The ratio of the areas of two similar figures is 4:9. What is the ratio of their perimeters? 30. Given: ||AD CB Prove: AE CE DE BE• = •

 

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10R Unit 8 Similarity CW 8.9 HW: Worksheet #8.9 (following these notes) Solving Quadratic Equations

EXAMPLES: Solve for x. Express your answers in simplest radical form.

 

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10R Unit 8 Similarity HW 8.9 Solving Quadratic Equations DIRECTIONS: Solve for x. Express your answers in simplest radical form. 1. x2 + 5x −14 = 0 2. 4x2 −13x + 3= 0 3. 2x2 + 7x + 3= 0 4. 5x2 + 2x − 2 = 0 5. 2x2 −10x +11= 0 6. 8x2 − 2x − 3= 0 7. x2 − 4x = 0 8. x2 − 25 = 0 9. 6x2 +10x = 5 10. 1= 2x2 − 6x

 

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10R Unit 8 Similarity - EXTRA FACTORING PRACTICE Factoring – Trinomials ax2 + bx + c where a 1, THE METHOD Practice: Factor Completely. 1. 2.

3. 4.

5. 6.

≠

2 11 52n n− + 6 5 14 2y y+ +

3 22a a− − 5 13 64 2b b− +

3 7 202x x+ − 12 352v v− −

 

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Mixed Practice: Factor Completely. 1.

2.

3.

4.

5. 6. 7.

8. 9. 10.

11. 12. 13.

m m2 22 121− + 3 18 272x x+ +

16 40 252y y− + rx rx r2 4 4− +

2 14 162x x+ − 16 814b − 2 9 72x x+ +

4 42c − 32 5003x − u u4 22+

x x2 12+ − 4 20 252y y+ + 28 5 34 2z z− −

 

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Factor Completely. 1. 2.

3. 4.

5. 6.

7. 8.

3 10 82m m+ − 12 28 242x x− −

− + −3 30 754 3 2x x x 6 19 102x x+ +

8 10 32x x− − 4 2 62x x− −

2 328x − − +12 272x