CHAPTER 7: Similar Figures - White Plains Public Schools / … · 2011-12-14 · 1 Day 1 - Chapter...
Transcript of CHAPTER 7: Similar Figures - White Plains Public Schools / … · 2011-12-14 · 1 Day 1 - Chapter...
CHAPTER 7: Similar Figures
TABLE CONTENTS
DAY 1: (Ch. 7-2) SWBAT: Identify and apply properties of similar polygons to solve problems.
Pgs: 1 - 5 HW: Pgs: 6 - 7
DAY 2: (Ch. 7-4) SWBAT: Apply Three Theorems frequently used to establish proportionality
Pgs: 8 - 13
HW: Pgs: 14 - 16
DAY 3: (8-1) SWBAT: Apply Properties of Similar Right Triangles to Solve Problems Pgs: 17 - 24
HW: Pgs: 25 - 27
DAY 4: (8-1) SWBAT: Apply Properties of Similar Right Triangles to Solve Problems Pgs: 28 - 32
HW: Finish this section for homework
DAY 5: SWBAT: Review problems involving Similar Figures
Pgs: 33 - 39
HW: Finish this section for homework
Day 6: EXAM
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Day 1 - Chapter 7-2: Similar Polygons
SWBAT: Use proportions to solve problems
Identify and apply properties of similar polygons to solve problems.
Warm – Up
1) The ratio of the angles in a quadrilateral are 2 : 3 : 5 : 10, What is the measure of the largest angle?
Figures that are similar (~) have the same shape but not necessarily the same size.
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Example 1:
Given: ∆ABC ∆DEF
Each pair of corresponding angles are congruent:
______ ______ ______
The ratios of the measures of all pairs of corresponding sides are equal:
Determine whether the following polygons are similar. If they are, write a similarity statement.
1.
2.
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Example 2:
If ∆ABC ∼ ∆ZXY, m A = 60, and m B = 85, what is m Y?
You Try It!
a. If ∆DEF ∼ ∆GHI, m G = 110, and m E = 25, what is m F?
b. Given that and m m
Find the values of x and y.
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Example 3:
Given: ABCD EFGH Part a) Find: FG = _____ GH = _____ EH = _____ = ______ ______ ______ ______ Part b) Find the ratio of the perimeter of ABCD and the perimeter of EFGH.
You Try It!
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Challenge The two triangles are similar below. Solve for x.
SUMMARY Exit Ticket
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Homework
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12) 13) 14) 15) Given: m m SV = 15, NR = 20, RP = 10 Find: m , m , and VT 16)
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Day 2 – Chapter 7-3: Triangle Proportionality Theorem
SWBAT: Apply Three Theorems frequently used to establish proportionality
Warm – Up
1. If ∆ABC ∆PQR, find x and y.
2. The ratio of two sides of similar triangles is 1:3. The perimeter of the smaller triangle is 22
cm, find the perimeter of the larger triangle.
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Side Splitter Theorem
Conclusion:
Example 1:
Example 2:
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You Try It! Solve for x.
Example 3:
You Try It!
In D is a point on and E is a point on such that . If BE = 4, EC = 8, and DE = 6, find the length of .
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Parallels Proportion Theorem
Given:
Conclusion:
Example 4:
You Try It!
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Angle Bisector Proportionality Theorem
Conclusion:
Ex 5.
You Try It!
Challenge Solve for x.
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SUMMARY
Exit Ticket
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Day 2 – Homework
Solve for all of the missing sides. Show the proportions used.
2)
3) Solve for x.
4) Solve for x.
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5) Solve for x.
6) Solve for x.
7) CHALLENGE!!!!! Solve for x.
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8) Vcv
9) In M is a point on and N is a point on such that . If FN = 3, NE = 6, and MN = 4, find the length of .
10) In M is a point on and N is a point on such that . If MF = 4, DF = 8, and DE = 10, find the length of .
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Day 3 - Similarities in Right Triangles
Warm - Up
Solve for x.
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Similarities in Right Triangles
______ ______ ______
From above, you know that altitude
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Rules:
Rule #1: Altitude Rule
So,
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Example 1: Solve for x.
You Try It!
You Try It!
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Rule #2: Leg Rule
So,
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Example 2: Solve for x.
Example 3:
You Try It!
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Challenge: Solve for x
SUMMARY
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Exit Ticket
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2.
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Day 3 – HW
Similarities in Right Triangles
4)
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5) Find the value of x. 6)
7) Find the length of the altitude of PQR. 8) Find the length of HK of right triangle GHK.
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9) Challenge!!!! Solve for x.
10) 11) Fgfg
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Day 4 – Similarities in Right Triangles – Day 2
Warm – Up
1.
2. Hjh
3.
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Regents Level Questions 4.
5. You Try It!
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6) 7) Fdfdf 8) hjh
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SUMMARY: Solving a Quadratic Equation with Similar Right Triangles
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Day 5 – Review of Similar Triangles
Section 1: Similar Polygons Determine whether each pair of figures is similar. If so, write a similarity statement and scale factor. If not explain your reasoning. 1.
2. 3.
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4.
5.
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7.
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Section 2: Proportional Parts in Similar Triangles 8.
9. Find x
10. Solve for y.
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11.
12. Solve for x.
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Section 3: Geometric Mean and Similarities in Right Triangles 13.
14. Find x.
15. Fdfd
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16.
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18. Extended Response Regents Level Question.