(8) Lesson 7.5 - Similar Triangles and Indirect measurement

1. Course 3, Lesson 7-5
1. Determine whether the pair of polygons is similar. Explain.
2. The pair of polygons is similar. Determine the missing side
measure.
3. A greeting card is 8 inches by 6 inches, but it will have to be cut to
fit in an envelope. The scale factor from the original card to the
smaller card is 5:4. Determine the dimensions of the smaller card.

2. Course 3, Lesson 7-5
ANSWERS
1. No; corresponding sides are not proportional.
2.
3. ×
3
; 4.5
4 6
 
x
x
2
6
5
4
4
5

3. HOW can you determine
congruence and similarity?
Geometry
Course 3, Lesson 7-5

4. Course 3, Lesson 7-5 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
• 8.G.5
Use informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.
Geometry

5. To
• write similarity statements for similar
triangles,
• use indirect measurement to find
missing measures on a right triangle
Course 3, Lesson 7-5
Geometry

6. • indirect measurement
Course 3, Lesson 7-5
Geometry

7. Course 3, Lesson 7-5
Geometry
Words If two angles of one triangle are congruent to two angles of
another triangle, then the triangles are similar.
Symbols If
Model
, , .A F B G ABC FGH     and then

8. 1
Need Another Example?
Step-by-Step Example
1. Determine whether the triangles are similar. If so, write a
similarity statement.
Angle A and ∠E have the same measure, so they are congruent. Since
180 – 62 – 48 = 70, ∠G measures 70°. Two angles of EFG are
congruent to two angles of ABC, so ABC ~ EFG.

9. Answer
Need Another Example?
Determine whether the triangles are similar. If
so, write a similarity statement.
The triangles are not similar.

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. A fire hydrant 2.5 feet
high casts a 5-foot
shadow. How tall is a
street light that casts a
26-foot shadow at the
same time? Let h
represent the height of
the street light.
Shadow Height
hydrant hydrant
street light street light
=
5 2.5
h26
5h = 26 • 2.5
5h = 65
Find the cross products.
Multiply.
Divide each side by 5.
The street light is 13 feet tall.
h = 13

11. Answer
Need Another Example?
How tall is the flagpole?
38.5 ft

12. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. In the figure at the
right, triangle DBA is
similar to triangle
ECA. Ramon wants
to know the distance
across the lake.
320d = 482 • 40
d = 60.25
AB corresponds to AC and BD corresponds to CE.
Find the cross products.
The distance across the lake is 60.25 meters.
Replace AB with 320, AC with 482, and BD with 40.
Multiply. Then divide each side by 320.

13. Answer
Need Another Example?
The two triangles in the figure are similar. Find
the distance across the lake.
15 m

14. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-5
Geometry

15. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-5
Geometry
Sample answer:
• In triangles, if two angles of one triangle are congruent
to two angles of another triangle, the two triangles are
similar.

16. How did yesterday’s lesson
about similar triangles
help you to learn about
angle-angle-similarity?
Course 3, Lesson 7-5
Ratios and Proportional RelationshipsFunctionsGeometry