1. Five-Minute Check (over Lesson 7–2) Mathematical Practices Then/Now
Postulate 7.1: Angle-Angle (AA) Similarity
Example 1: Use the AA Similarity Postulate
Example 2: Sufficient Conditions
Theorem 7.2: Properties of Similarity
Example 3: Parts of Similar Triangles
Example 4: Real-World Example: Indirect Measurement
Lesson Menu

2. Determine whether the triangles are similar.
Yes, corresponding angles are congruent and corresponding sides are proportional.
B. No, corresponding sides are not proportional.
5-Minute Check 1

3. The quadrilaterals are similar
The quadrilaterals are similar. Find the scale factor of the larger quadrilateral to the smaller quadrilateral.
A. 5:3
B. 4:3
C. 3:2
D. 2:1
5-Minute Check 2

4. The triangles are similar. Find x and y.
A. x = 5.5, y = 12.9
B. x = 8.5, y = 9.5
C. x = 5, y = 7.5
D. x = 9.5, y = 8.5
5-Minute Check 3

5. Determine whether Figure A and Figure B are similar. Explain.
Yes; map Figure A to Figure B using a dilation centered at the origin with a scale
factor of B. C.
factor of followed by a translation along <–1, 0>. D.
No; the figures do not have the same shape.
5-Minute Check 4

6. Two pentagons are similar with a scale factor of
Two pentagons are similar with a scale factor of The perimeter of the larger pentagon is 42 feet. What is the perimeter of the smaller pentagon? __ 3 7
A. 12 ft
B. 14 ft
C. 16 ft
D. 18 ft
5-Minute Check 5

7. Mathematical Processes
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Content Standards
G.SRT.2 Given two figures, use the definition of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. MP

8. G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MP

9. You used the properties of similarity to compare polygons.
Use the AA similarity criterion to prove triangles similar.
Solve problems by using the properties of similar triangles.
Then/Now

10. Postulate

11. Use the AA Similarity Postulate
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. A.
Example 1

12. Use the AA Similarity Postulate
Triangle Sum Theorem: 180 – 42 – 58 = 80
mA = 80°
A ≅ E, B ≅ D
Given angles
AA Similarity.
Answer: By the Triangle Sum Theorem, mA = 80. Because A ≅ E and B ≅ D, ABC ∼ EDF by AA Similarity.
Example 1

13. Use the AA Similarity Postulate
Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. B.
Example 1

14. Vertical angles are congruent. QXP ≅ NXM
Use the AA Similarity Postulate
QXP ≅ NXM
Vertical angles are congruent.
Q ≅ N
Alternate interior angles are congruent.
AA Similarity.
Answer: By the Vertical Angles Theorem, QXP ≅ NXM, and because, Q ≅ N. Therefore, QXP ∼ NXM by AA Similarity.
Example 1

15. QRS and WXY are isosceles triangles.
Sufficient Conditions
QRS and WXY are isosceles triangles.
Which of the following is an incorrect statement? Which of the following would not be sufficient to prove that QRS ∼ WXY?
A. QRS ≅ WXY
B. QRS ≅ WXY
C. QRS and WXY are the vertex angles and QRS ≅ WXY .
D. QRS and WXY are base angles and QRS ≅ WXY .
Example 2

16. Sufficient Conditions
QRS and WXY are isosceles triangles. In isosceles triangles the base angles are congruent.
All of the statements listed are true. Now decide which statement is not sufficient to prove the triangles are similar.
Choice A: States that the triangles are congruent. If the triangles are congruent then they are also similar.
Choices C and D: Are statements about the vertex angles and base angles of the triangles which prove an isosceles triangle are congruent by the AA theorem. If the triangles are congruent then they are also similar.
Example 2

17. Sufficient Conditions
Choice B: Only states that one angle is congruent. It is not sufficient to prove the triangles are similar.
Answer: B
Example 2

18. Theorem

19. Parts of Similar Triangles
Algebra Given RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10. Find RQ and QT.
Write a proportion that relates to the corresponding sides.
Example 3

20. Substitute the lengths of the sides.
Parts of Similar Triangles
Substitute the lengths of the sides.
Solve for x.
RQ = x + 3 = = 8
QT = 2x + 10 = 2(10) + 10 = 20
Answer: 8; 20
Example 3

21. Indirect Measurement
SKYSCRAPERS Josh wanted to measure the height of the Willis Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1:00 p.m. The length of the shadow was 2 feet. Then he measured the length of Willis Tower’s shadow and it was 242 feet at the same time. What is the height of the Willis Tower?
Example 4

22. Write a proportion that relates to the corresponding sides.
Indirect Measurement
Write a proportion that relates to the corresponding sides.
Answer: 1452 ft (actual height: 1450 feet)
Example 4