The document is a lesson on similar figures in geometry. It defines similar figures as two or more figures that have the same shape but may be different sizes. It also defines corresponding sides and angles. The lesson then provides three example problems asking students to use proportions to find missing side lengths and angle measures in similar triangles.

1. Name ______________________________ Date _____________________
Mrs. Labuski / Mrs. Rooney Period ____ Lesson 8-4 Similar Figures
VOCABULARY DEFINITION EXAMPLE
Two or more figures are
similar if they have
Similar exactly the same shape.
They may be different
sizes.
Have lengths that are
Corresponding
proportional
Sides
PQ
QR
PR
Angles that are congruent
Corresponding
(Same size and same
Angles
shape) P
Q
R
Use a proportion to find the missing length.
triangle 1 triangle 2
FG = GH AB = JK
VW WX AC JL
_2__ = _8 5 = 10
6 x 13 x
2x = 48 5x = 130
x = 24 x = 26

2. 1. The two triangles are similar. Find the missing length x and the measure of ∠A.
20 = 12 32 180
30 x
20x = 360
+68 -100
÷20 ÷20 100 80
x = 18 ∠A 80◦
DF = 18 ft
2. The two triangles are similar. Find the missing length x and the measure of ∠J.
NP = PM 122 180
JK KH +35 -157
157 23
10 = x
15 12 ∠J 23◦
15x = 120
÷15 ÷15
x=8
PM = 8m

3. 3. The two triangles are similar. Find the missing length x and the measure of ∠N.
60 180
ML = MN +67 -127
JG JH 127 53
10 = 12
20 x
∠N 53◦
10x = 240
÷10 ÷10
x = 24
JH = 24cm

4. Name ______________________________ Date _____________________
Mrs. Labuski / Mrs. Rooney Period ____ Lesson 8-4 Similar Figures
VOCABULARY DEFINITION EXAMPLE
Similar
Corresponding
Sides
Corresponding
Angles
Use a proportion to find the missing length.
FG = GH
VW WX
___ = ____

5. 1. The two triangles are similar. Find the missing length x and the measure of ∠A.
2. The two triangles are similar. Find the missing length x and the measure of ∠J.

6. 3. The two triangles are similar. Find the missing length x and the measure of ∠N.