Geometry 8 1 Similarity in right triangles - Wikispaces8_1...13.2 and 8 14. 10 and 30 15. 8 and 9...
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Attendance Problems. Term Definition 1. _____ Altitude A. A comparison of two numbers by division B. A segment from a vertex to the midpoint 2. _____ Proportion B. A segment from a vertex to the midpoint of the opposite side of a triangle C. An equation stating that two ratios are 3. _____ Ratio equal D. A perpendicular segment from the vertex of a triangle to a 4. _____ Right Triangle vertex of a triangle to a line containing the base E. A triangle that contains a right angle. 5. Are the two triangles similar? Explain why or why not. Find the value of x. Give the answer in simplest radical form. 6. 7. 8. J K L 5 45 ˚ x P Q R 16 45 ˚ x E G F 4 30 ˚ x P S T Q R 12 10 6 5 Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 1 of 9
Transcript of Geometry 8 1 Similarity in right triangles - Wikispaces8_1...13.2 and 8 14. 10 and 30 15. 8 and 9...
Attendance Problems. Term Definition
1. _____ AltitudeA. A comparison of two numbers by division B. A segment from a vertex to the midpoint of the opposite side of a triangle C. An equation stating that two ratios are equal D. A perpendicular segment from the vertex of a triangle to a line containing the base E. A triangle that contains a right angle.
2. _____ Proportion
A. A comparison of two numbers by division B. A segment from a vertex to the midpoint of the opposite side of a triangle C. An equation stating that two ratios are equal D. A perpendicular segment from the vertex of a triangle to a line containing the base E. A triangle that contains a right angle.
3. _____ Ratio
A. A comparison of two numbers by division B. A segment from a vertex to the midpoint of the opposite side of a triangle C. An equation stating that two ratios are equal D. A perpendicular segment from the vertex of a triangle to a line containing the base E. A triangle that contains a right angle.4. _____ Right Triangle
A. A comparison of two numbers by division B. A segment from a vertex to the midpoint of the opposite side of a triangle C. An equation stating that two ratios are equal D. A perpendicular segment from the vertex of a triangle to a line containing the base E. A triangle that contains a right angle.
5. Are the two triangles similar? Explain why or why not.
Find the value of x. Give the answer in simplest radical form. 6.� � � � � 7.� � � � � 8.
A. a comparison of two numbers by division
B. a segment from a vertex to the midpoint of the opposite side of a triangle
C. an equation stating that two ratios are equal
D. a perpendicular segment from the vertex of a triangle to a line containing the base
E. a triangle that contains a right angle
VocabularyMatch each term on the left with a definition on the right. 1. altitude
2. proportion
3. ratio
4. right triangle
Identify Similar FiguresDetermine if the two triangles are similar.
5. P S
T Q R
12
10 6
5
6. A
B C
D
E F
15
4
10 6
Special Right TrianglesFind the value of x. Give the answer in simplest radical form.
7. J
K L
5
45˚
x
8. P Q
R
16 45˚
x
9.
E
G
F
4 30˚
x
10.
A
C
B
60˚ 3 x
Solve Multi-Step EquationsSolve each equation. 11. 3 (x - 1) = 12 12. -2 (y + 5) = -1
13. 6 = 8 (x - 3) 14. 2 = -1 (z + 4)
Solve ProportionsSolve each proportion. 15. 4 _ y = 6 _
18 16. 5 _
8 = x _
32 17. m _
9 = 8 _
12 18.
y _
4 = 9 _ y
Rounding and EstimationRound each decimal to the indicated place value. 19. 13.118; hundredth 20. 37.91; tenth
21. 15.992; tenth 22. 173.05; whole number
Right Triangles and Trigonometry 531
CS10_G_MESE612294_C08AR.indd 531CS10_G_MESE612294_C08AR.indd 531 2023011 4:06:52 PM2023011 4:06:52 PM
� � �
A. a comparison of two numbers by division
B. a segment from a vertex to the midpoint of the opposite side of a triangle
C. an equation stating that two ratios are equal
D. a perpendicular segment from the vertex of a triangle to a line containing the base
E. a triangle that contains a right angle
VocabularyMatch each term on the left with a definition on the right. 1. altitude
2. proportion
3. ratio
4. right triangle
Identify Similar FiguresDetermine if the two triangles are similar.
5. P S
T Q R
12
10 6
5
6. A
B C
D
E F
15
4
10 6
Special Right TrianglesFind the value of x. Give the answer in simplest radical form.
7. J
K L
5
45˚
x
8. P Q
R
16 45˚
x
9.
E
G
F
4 30˚
x
10.
A
C
B
60˚ 3 x
Solve Multi-Step EquationsSolve each equation. 11. 3 (x - 1) = 12 12. -2 (y + 5) = -1
13. 6 = 8 (x - 3) 14. 2 = -1 (z + 4)
Solve ProportionsSolve each proportion. 15. 4 _ y = 6 _
18 16. 5 _
8 = x _
32 17. m _
9 = 8 _
12 18.
y _
4 = 9 _ y
Rounding and EstimationRound each decimal to the indicated place value. 19. 13.118; hundredth 20. 37.91; tenth
21. 15.992; tenth 22. 173.05; whole number
Right Triangles and Trigonometry 531
CS10_G_MESE612294_C08AR.indd 531CS10_G_MESE612294_C08AR.indd 531 2023011 4:06:52 PM2023011 4:06:52 PM
� � �
A. a comparison of two numbers by division
B. a segment from a vertex to the midpoint of the opposite side of a triangle
C. an equation stating that two ratios are equal
D. a perpendicular segment from the vertex of a triangle to a line containing the base
E. a triangle that contains a right angle
VocabularyMatch each term on the left with a definition on the right. 1. altitude
2. proportion
3. ratio
4. right triangle
Identify Similar FiguresDetermine if the two triangles are similar.
5. P S
T Q R
12
10 6
5
6. A
B C
D
E F
15
4
10 6
Special Right TrianglesFind the value of x. Give the answer in simplest radical form.
7. J
K L
5
45˚
x
8. P Q
R
16 45˚
x
9.
E
G
F
4 30˚
x
10.
A
C
B
60˚ 3 x
Solve Multi-Step EquationsSolve each equation. 11. 3 (x - 1) = 12 12. -2 (y + 5) = -1
13. 6 = 8 (x - 3) 14. 2 = -1 (z + 4)
Solve ProportionsSolve each proportion. 15. 4 _ y = 6 _
18 16. 5 _
8 = x _
32 17. m _
9 = 8 _
12 18.
y _
4 = 9 _ y
Rounding and EstimationRound each decimal to the indicated place value. 19. 13.118; hundredth 20. 37.91; tenth
21. 15.992; tenth 22. 173.05; whole number
Right Triangles and Trigonometry 531
CS10_G_MESE612294_C08AR.indd 531CS10_G_MESE612294_C08AR.indd 531 2023011 4:06:52 PM2023011 4:06:52 PM
A. a comparison of two numbers by division
B. a segment from a vertex to the midpoint of the opposite side of a triangle
C. an equation stating that two ratios are equal
D. a perpendicular segment from the vertex of a triangle to a line containing the base
E. a triangle that contains a right angle
VocabularyMatch each term on the left with a definition on the right. 1. altitude
2. proportion
3. ratio
4. right triangle
Identify Similar FiguresDetermine if the two triangles are similar.
5. P S
T Q R
12
10 6
5
6. A
B C
D
E F
15
4
10 6
Special Right TrianglesFind the value of x. Give the answer in simplest radical form.
7. J
K L
5
45˚
x
8. P Q
R
16 45˚
x
9.
E
G
F
4 30˚
x
10.
A
C
B
60˚ 3 x
Solve Multi-Step EquationsSolve each equation. 11. 3 (x - 1) = 12 12. -2 (y + 5) = -1
13. 6 = 8 (x - 3) 14. 2 = -1 (z + 4)
Solve ProportionsSolve each proportion. 15. 4 _ y = 6 _
18 16. 5 _
8 = x _
32 17. m _
9 = 8 _
12 18.
y _
4 = 9 _ y
Rounding and EstimationRound each decimal to the indicated place value. 19. 13.118; hundredth 20. 37.91; tenth
21. 15.992; tenth 22. 173.05; whole number
Right Triangles and Trigonometry 531
CS10_G_MESE612294_C08AR.indd 531CS10_G_MESE612294_C08AR.indd 531 2023011 4:06:52 PM2023011 4:06:52 PM
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 1 of 9
9.
A. a comparison of two numbers by division
B. a segment from a vertex to the midpoint of the opposite side of a triangle
C. an equation stating that two ratios are equal
D. a perpendicular segment from the vertex of a triangle to a line containing the base
E. a triangle that contains a right angle
VocabularyMatch each term on the left with a definition on the right. 1. altitude
2. proportion
3. ratio
4. right triangle
Identify Similar FiguresDetermine if the two triangles are similar.
5. P S
T Q R
12
10 6
5
6. A
B C
D
E F
15
4
10 6
Special Right TrianglesFind the value of x. Give the answer in simplest radical form.
7. J
K L
5
45˚
x
8. P Q
R
16 45˚
x
9.
E
G
F
4 30˚
x
10.
A
C
B
60˚ 3 x
Solve Multi-Step EquationsSolve each equation. 11. 3 (x - 1) = 12 12. -2 (y + 5) = -1
13. 6 = 8 (x - 3) 14. 2 = -1 (z + 4)
Solve ProportionsSolve each proportion. 15. 4 _ y = 6 _
18 16. 5 _
8 = x _
32 17. m _
9 = 8 _
12 18.
y _
4 = 9 _ y
Rounding and EstimationRound each decimal to the indicated place value. 19. 13.118; hundredth 20. 37.91; tenth
21. 15.992; tenth 22. 173.05; whole number
Right Triangles and Trigonometry 531
CS10_G_MESE612294_C08AR.indd 531CS10_G_MESE612294_C08AR.indd 531 2023011 4:06:52 PM2023011 4:06:52 PM
Solve.10.2 = -(z + 4) 11. y
4=9y
Round each decimal to the indicated place value.12. 15.992; tenth 13. 173.05; whole number
•I can use geometric mean to find segment lengths in right triangles.
•I can apply similarity relationships in right triangles to solve problems.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 2 of 9
Common Core: CC.9-12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Right triangle activity. You will need to two colored pencils and a scissors.
In a right triangle, an altitude drawn from the vertex of the right angle to the hypotenuse forms two right triangles.
Example 1.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 3 of 9
12. Guided Practice. Write a similarity statement comparing the three triangles.
Consider the proportion ax= xb. In this case, the means of the
proportion are the same number, and that number is the geometric mean of the extremes. The geometric mean of two positive numbers is the positive square root of their product. So the geometric mean of a and b is the positive number x such thatx = ab , or x2 = ab.
Example 2. Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.A. 8 and 2 B. 5 and 15
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 4 of 9
Guided Practice. Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.13. 2 and 8 14. 10 and 30 15. 8 and 9
You write proportions comparing the side lengths of the triangles formed by the altitude to the hypotenuse of a right triangle.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 5 of 9
Example 3.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 6 of 9
Once you!ve found the unknown side lengths, you can use the Pythagorean Theorem to check your answers.
Helpful Hint
16. Guided Practice. Find u, v, and w.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 7 of 9
Example 4.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 8 of 9
17. Guided Practice. A surveyor positions himself so that his line of sight to the top of a cliff and his line of sight to the bottom form a right angle as shown. What is the height of the cliff to the nearest foot?
8-1 Assignment (pp 537-539) 16, 18, 24, 27, 30-36 even, 40-42, 44-47.
Pre-AP Geometry 8-1 Study Guide: Similarity in right triangles (pp 535-536) Page 9 of 9
