1. Similar Triangles
Chapter 7-3

2. Identify similar triangles.
Use similar triangles to solve problems.
Standards 4.0 Students prove basic theorems involving congruence and similarity. (Key)
Standard 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
Lesson 3 MI/Vocab

3. Triangle Similarity is:
Lesson 3 TH2

4. Writing Proportionality Statements
Given BTW ~ ETC
Write the Statement of Proportionality
Find mTEC
Find TE and BE T W B C E
34o 3 20
mTEC = mTBW = 79o
79o 12

5. AA  Similarity Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
If K  Y and J  X,
then  JKL ~  XYZ. K J L Y X Z

6. Example
Are these two triangles similar? Why? N M P Q R S T

7. SSS  Similarity Theorem
If the corresponding sides of two triangles are proportional, then the two triangles are similar. B A C Q P R

8. Which of the following three triangles are similar?J H G 6 14 10 F E D 6 8 4 A C B 12 6 9
ABC and FDE?
ABC~ FDE
SSS ~ Thm
Scale Factor = 3:2
Longest Sides
Shortest Sides
Remaining Sides

9. Which of the following three triangles are similar?J H G 6 14 10 F E D 6 8 4 A C B 12 6 9
ABC and GHJ
ABC is not similar to DEF
Longest Sides
Shortest Sides
Remaining Sides

10. SAS  Similarity Theorem
If one angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. K J L Y X Z
ass
Pantograph

11. Prove RTS ~ PSQ S  S (reflexive prop.) SPQ  SRT SAS  ~ Thm. S5 15 12 4
SPQ  SRT
SAS  ~ Thm.

12. Are the two triangles similar?P Q R T 10 15 12 9
NQP  TQR
Not Similar

13. How far is it across the river?
2 yds
5 yds
x yards
42 yds
2x = 210
x = 105 yds

14. Are Triangles Similar?
In the figure, , and ABC and DCB are right angles. Determine which triangles in the figure are similar.
Lesson 3 Ex1

15. by the Alternate Interior Angles Theorem.
Are Triangles Similar?
by the Alternate Interior Angles Theorem.
Vertical angles are congruent,
Answer: Therefore, by the AA Similarity Theorem, ΔABE ~ ΔCDE.
Lesson 3 Ex1

16. In the figure, OW = 7, BW = 9, WT = 17. 5, and WI = 22. 5
In the figure, OW = 7, BW = 9, WT = 17.5, and WI = Determine which triangles in the figure are similar.
A. ΔOBW ~ ΔITW
B. ΔOBW ~ ΔWIT
C. ΔBOW ~ ΔTIW
D. ΔBOW ~ ΔITW
Lesson 3 CYP1

17. Parts of Similar Triangles
ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.
Lesson 3 Ex2

18. Parts of Similar Triangles
Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons,
Substitution
Cross products
Lesson 3 Ex2

19. Parts of Similar Triangles
Distributive Property
Subtract 8x and 30 from each side.
Divide each side by 2.
Now find RQ and QT.
Answer: RQ = 8; QT = 20
Lesson 3 Ex2

20. A. ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.
Lesson 3 CYP2

21. B. ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find CE.
Lesson 3 CYP2

22. What is the height of the Sears Tower?
Indirect Measurement
INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time.
What is the height of the Sears Tower?
Lesson 3 Ex3

23. Indirect Measurement
Since the sun’s rays form similar triangles, the following proportion can be written.
Now substitute the known values and let x be the height of the Sears Tower.
Substitution
Cross products
Lesson 3 Ex3

24. Interactive Lab: Cartography and Similarity
Indirect Measurement
Simplify.
Divide each side by 2.
Answer: The Sears Tower is 1452 feet tall.
Interactive Lab: Cartography and Similarity
Lesson 3 Ex3

25. INDIRECT MEASUREMENT On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot?
A. 196 ft B ft
C. 441 ft D ft
Lesson 3 CYP3

26. Homework
Chapter 7-3
Pg 400
7 – 17, 21, 31 – 38