CHAPTER 8: Similar Polygons
Geometry Honors
TABLE CONTENTS

DAY 1: (Ch. 8-1) SWBAT: Apply the theorems associated with ratios
Pgs: 1 - 4
HW: Page 330 in Honors Textbook #3, 4b, 4c, 7-9, 10-14, 17, 19, 21

DAY 2: (Ch. 8 - 2) SWBAT: Identify the characteristics of similar figures
Pgs: 5 - 9
HW: Page 336 in Honors Textbook #2-6, 8-14, 18

DAY 3: (8 - 3)
SWBAT: Use Several Methods to prove that triangles are similar.
Pgs: 10 - 14
HW: Page 341 in Honors Textbook #2-5, 11, 16, 18, 19, and 22

DAY 4: (8 - 4)
SWBAT: Use the concept of similarity to establish the congruence of angles
and the proportionality of segments
Pgs: 15 - 18
HW: 347 in Honors Textbook #1-5, 7, 12, 16, 17-20, 22

DAY 5: (8 - 5)
SWBAT: Apply Three Theorems frequently used to establish
proportionality
Pgs: 19 - 24
HW: Page 354 in Honors Textbook #1-13, 15-16, 23-24


DAY 6: (8-3 to 8-5) SWBAT: Use Several Methods to prove that triangles are similar.
Pgs: 25 - 27
HW: Finish this section
DAY 7: (9 -3)
SWBAT: Apply Properties of Similar Right Triangles to Solve Problems
Pgs: 28 - 35
HW: 379 in Honors Textbook #1-7, and 16

DAY 8: (9 -3)
SWBAT: Apply Properties of Similar Right Triangles to Solve Problems – Day 2
Pgs: 36 - 40
HW: Finish this section for homework

Day 9: (Review)
Pgs: 41-49
1
Day 1- Chapter 8–1: Ratios and Proportions
SWBAT: Use proportions to solve problems
Apply the product and ratio theorems
Warm – Up
1)
2) The ratio of the side lengths of a quadrilateral is 2 : 3 : 5 : 7, and its perimeter
is 85 ft. What is the length of the longest side?
3) The ratio of the angle measures in a triangle is 1 : 6 : 13.What is the measure of
each angle?
1
2
3
Challenge
Summary
Exit Ticket
4
Day 2- Chapter 8–2: Similarity
SWBAT: Identify the characteristics of similar figures
Warm – Up
Solve for x.
Figures that are similar (~) have the same shape but not necessarily the same size.
5
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.
a.
b.
6
Example 2:
If ∆ABC ∼ ∆ZXY, m A = 60, and m B = 85, what is m Y?
Example 3:
Given: BAT  DOT
OT = 15, BT = 12, TD = 9
Find the length of AO.
Example 4:
Given that
and m
Find the values of x and y.
m
7
Example 5:
Given: ABCD  EFGH
Part a) Find:
FG = _____
GH = _____
EH = _____
= ______
______
______
______
Part b) Find the ratio of the perimeter of ABCD and the perimeter of EFGH.

Example 6:
8
Challenge
SUMMARY
Exit Ticket
9
Day 3- Chapter 8–3: Methods of Proving Triangles Similar
SWBAT: Use several methods to prove that triangles are similar.
Warm - Up
1)
2) Given:
m
m
SV = 15, NR = 20, RP = 10
Find: m
,m
, and VT
10
11
Example 3: Explain why the triangles below are similar.
Example 4: Explain why the triangles below are similar.
12
13
Summary
Exit Ticket
M is the midpoint of JK. N is the midpoint of KL
and P is the midpoint of JL.
Which method can be used to show that JKL
must be similar to NPM?
14
Day 4- Chapter 8–4: Congruences and Proportions in Similar Triangles
SWBAT: Use the concept of similarity to establish the congruence of angles and the proportionality of
segments.
Warm – Up
15
Example 1:
Example 2:
Example 3:
16
Example 5:
17
Summary
Exit Ticket
18
Day 5 – Chapter 8-4: 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.
19
Side Splitter Theorem
Conclusion:
Example 1:
Example 2: Solve for x.
20
Example 3:
Parallels Proportion Theorem
Given:
Conclusion:
Example 4:
21
Angle Bisector Proportionality Theorem
Conclusion:
Ex 5.
22
Proofs
Ex 6:
Ex 7:
23
SUMMARY
Exit Ticket
24
Day 6 – Practice writing Similar Triangle Proofs
SWBAT: Use several methods to prove triangles are similar.
Warm – Up
25
26
Prove:
27
Day 7 – Similarities in Right Triangles
SWBAT: Identify the relationships between parts of a right triangle when an altitude is
drawn to the hypotuenuse.
Similarities in Right Triangles
______  ______  ______
28
From the above, you know that altitude
29
Rules:
Rule #1: Altitude Rule
So,
30
Example 1: Solve for x.
You Try It!
You Try It!
31
Rule #2: Leg Rule
So,
32
Example 2: Solve for x.
Example 3:
You Try It!
33
Challenge: Solve for x
SUMMARY
34
Exit Ticket
1.
2.
35
Day 8 – Similarities in Right Triangles – Day 2
SWBAT: Identify the relationships between parts of a right triangle when an altitude is
drawn to the hypotenuse.
Warm – Up
1.
2. Hjh
3.
36
37
Regents Level Questions
4.
5. You Try It!
38
6)
7)
Fdfdf
8)
hjh
39
SUMMARY: Solving a Quadratic Equation with Similar Right Triangles
40
Day 9 – 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.
41
4.
5.
42
6.
7.
43
Section 2: Proportional Parts in Similar Triangles
8.
9.
10.
Solve for y.
44
11.
12.
df
13.
45
Section 3: Proving Triangles Similar
18.
46
19.
20.
47
21.
22.
48
Section 4: Geometric Mean and Similarities in Right Triangles
23.
24.
25.
26.
27.
49
ANSWER KEY
50