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True or false?
1. Some trapezoids are parallelograms.
false
2. Some figures with 4 right angles are
squares.
true
3. Some quadrilaterals have only one right
angle.
true
3/18/2015 8-3 D Similar & Congruent Figures
• 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
corresponding sides-
matching sides of
corresponding angles-
matching angles
two or more polygons
Example 1
The two triangles are similar. Find the
missing length y and the measure of D.
100
111
____
= ___
200
y
200 • 111 = 100 • y
The two triangles are similar. Find the
missing length y and the measure of D.
22,200 = 100y
22,200 = ____
100y
______
100
100
222 mm = y
Angle D is congruent to angle C, and m
m
D = 70°
C = 70°.
Example 2
The two triangles are similar. Find the
missing length y and the measure of B.
A 60 m
65°
50 m
45° 52 m
B
120 m
100 m
y
50
52
____
___
=
100
y
100 • 52 = 50 • y
The two triangles are similar. Find the
missing length y and the measure of B.
5,200 = 50y
5,200 = 50y
_____
___
50
50
104 m = y
Angle B is congruent to angle A, and m
65°.
m
B = 65°
A=
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?
Draw a diagram to represent the situation.
Use the corresponding sides to write a
proportion.
Actual
Reduced
2
54
3
w
2 cm
3 cm
_____
=
w cm
54 cm
54 • 3 = 2 • w
162 = 2w
162
2w
____
___
=
2
2
81 = w
The width of the actual painting is 81 cm.
Exit Ticket
These two triangles are similar.
1. Find the missing length x. 30 in.
2. Find the measure of
J. 36.9°
3. Find the missing length y.
4. Find the measure of
P.
4 in.
90°
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?
12 ft
1. These two triangles are similar. Identify
the missing length x.
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
2. These two triangles are similar. Identify
the measure R.
A. 30
B. 50
C. 80
D. 90
3. These two triangles are similar. Identify
the missing length y.
A. 27 in.
B. 21 in.
C. 9 in.
D. 8 in.
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
congruent figures-
have the same shape
and same size
-the corresponding sides and corresponding
angles are congruent.
Example 1
Decide whether the figures in each pair are
congruent. If not, explain.
These figures are NOT congruent.
Example 2
These figures are congruent.
Example 3
These figures are congruent.
Example 4
These figures are congruent.
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.
Exit Ticket
True or false?
1. If two figures have sides of the same length,
they are congruent. false
2. Congruent figures have angle measures that
are equal. true
3. Decide whether the figures are congruent. If
not, explain.
No; both are quadrilaterals
but they are not the same
size or shape.
Homework
• Pg. 483 #1-32 Evens
• Study quiz tomorrow!!!