1. Do Now True or false? 1. Some trapezoids are parallelograms.
2. Some figures with 4 right angles are squares.
3. Some quadrilaterals have only one right angle.
false
true
true

2. 3/18/2015 8-3 D Similar & Congruent Figures

3. Similar figures- have the same shape but not necessarily the same size
The measures of the corresponding angles are equal
The ratios of the lengths of the corresponding sides are proportional

4. corresponding sides- matching sides of two or more polygons
corresponding angles- matching angles

5. Example 1
The two triangles are similar. Find the missing length y and the measure of D.
100
200
____
111 y
___ =
200 • 111 = 100 • y

6. The two triangles are similar
The two triangles are similar. Find the missing length y and the measure of D.
22,200 = 100y
22,200
100
______
100y
100
____ =
222 mm = y
Angle D is congruent to angle C, and m C = 70°.
m D = 70°

7. Example 2
The two triangles are similar. Find the missing length y and the measure of B. B A
60 m
120 m
65°
50 m
100 m
45°
52 m y 50
100
____ 52 y
___ =
100 • 52 = 50 • y

8. The two triangles are similar
The two triangles are similar. Find the missing length y and the measure of B.
5,200 = 50y
5,200 50
_____
50y 50
___ =
104 m = y
Angle B is congruent to angle A, and m A = 65°.
m B = 65°

9. Example 3
This reduction is similar to a picture that Nicole painted. The height of the actual painting is 54 centimeters. What is the width of the actual painting?

10. Draw a diagram to represent the situation
Draw a diagram to represent the situation. Use the corresponding sides to write a proportion.
Actual
Reduced 2 54 3 w

11. 3 cm
w cm
2 cm
54 cm
_____ =
54 • 3 = 2 • w
162 = 2w
162 2
____ 2w 2
___ =
81 = w
The width of the actual painting is 81 cm.

12. Exit Ticket These two triangles are similar.
1. Find the missing length x.
2. Find the measure of J.
3. Find the missing length y.
4. Find the measure of P.
5. Susan is making a wood deck from plans for an 8 ft by 10 ft deck. However, she is going to increase its size proportionally. If the length is to be 15 ft, what will the width be?
30 in.
36.9°
4 in.
90°
12 ft

13. 1. These two triangles are similar. Identify the missing length x.
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm

14. 2. These two triangles are similar. Identify the measure R.
B. 50
C. 80
D. 90

15. 3. These two triangles are similar. Identify the missing length y.
A. 27 in.
B. 21 in.
C. 9 in.
D. 8 in.

16. 4. A carpenter is making a rectangular table top of dimensions 9 ft by 12 ft. However, he is going to increase its size proportionally. If the width is to be 15 ft, what will the length be?
A. 24 ft
B. 20 ft
C. 18 ft
D. 12 ft

17. congruent figures- have the same shape and same size
-the corresponding sides and corresponding angles are congruent.

18. Example 1
Decide whether the figures in each pair are congruent. If not, explain.
These figures are NOT congruent.

19. Example 2
These figures are congruent.

20. Example 3
These figures are congruent.

21. Example 4
These figures are congruent.

22. Example 5
Jodi needs a sleeping pad that is congruent to her sleeping bag. Which pad should she buy?
Sleeping pad B is congruent to the sleeping bag.

23. Exit Ticket True or false?
1. If two figures have sides of the same length, they are congruent.
2. Congruent figures have angle measures that are equal.
3. Decide whether the figures are congruent. If not, explain.
false
true
No; both are quadrilaterals but they are not the same size or shape.

24. Homework
Pg. 483 #1-32 Evens
Study quiz tomorrow!!!