Pre-Algebra
Congruent and Similar Figures Review
Name: _____________________________________
Date: _______________________
Per.: ________
1) In your own words, explain the difference between congruent and similar figures. In your explanation, discuss how you can find if
two figures are similar. Use diagrams to support your explanation.
ΔABC  ΔPQR.
2) Name all pairs of congruent sides.
C
P
3) Name all pairs of congruent angles.
Q
4m
3m
4) Find the measure of
 R.
B
50°
A
2m
R
5) Find the length of PQ .
Draw and label similar figures to answer each question.
6) A rectangular pool has a length of 20 feet and a width of 15 feet. Draw two other rectangular pools, one that is similar to the
original pool and one that isn’t similar. Explain how you can tell that your pools are similar and not similar to the original pool.
7) A 9-foot street sign casts a 12-foot shadow. The lamppost next to it casts a 24-foot shadow. How tall is the lamppost?
8) The manager of an amusement park wants to add a go-kart track that includes a bridge over a lake. Use the picture of the lake and
similar triangles to find the width of the lake.
F
x
90 ft
G
360 ft
H
J
45 ft
K
Transformations
9) a. Write a description of the rule ( x, y)  ( x  10, y  8). How is it telling you to move?
b. If the preimage contains the point (-2, 3), what is the image of the same point using the translation from part (a)?
10) Translate ΔXYZ two units to the left. Graph and label ΔX’Y’Z’, and write its coordinates below.
X’ ____________
Y’ ____________
Z’ ____________
11) Suppose this triangle was reflected over the y-axis and formed ΔH’J’K’.
a. If ΔHJK is reflected over the y-axis to form ΔH’J’K’, what are
the coordinates of vertex K’?
b. If ΔHJK is reflected over the x-axis to form ΔH”J”K”, what are
the coordinates of vertex K”?
c. Compare what happens to the coordinates of vertex K when it is
reflected over the y-axis to when it is reflected over the x-axis.
12) Rotate the rectangle below clockwise about the origin. Complete the table with the correct ordered pairs.
Preimage
90°
180°
270°
(0, 0)
(0, 2)
(6, 2)
(6, 0)
Explain what happens to each ordered pair after each 90° rotation clockwise
about the origin. What patterns do you notice?
13) ΔRUN is dilated to form ΔR’U’N’.
a. Graph the triangles on the coordinate grid.
ΔRUN
ΔR’U’N’
(6, 4)
(3, 2)
(-8, 0)
(-4, 0)
(2, -2)
(1, -1)
What is the scale factor?
b. Draw and label ΔR”U”N” after a translation of ΔR’U’N’ using
the rule ( x, y )  ( x  2, y  5) .
c. Is ΔR”U”N” congruent to ΔRUN? Is ΔR”U”N” congruent to ΔR’U’N’? How can you tell?
14) Describe how you could move the figure to exactly match the dashed figure using a series of two transformations.
Answer Key
1) Congruent figures are the same size and same shape. Similar figures are the same shape but not necessarily the same size. You can
find if two figures are similar if their corresponding sides are proportional to each other. This means that sides in one figure must
multiplied or divided by the same scale factor to create another figure that is proportional.
2) AB and PQ ; BC and QR ; AC and PR
3) A  P ; B  Q ; C  R
4) 40°
5) 2 m
6) Answers will vary.
7) 18 ft
8)180 ft
9) a. Move 10 units right and 8 units up.
b. (8, 11)
10) X’(-3, 1); Y’(2, 4); Z’(0, -2)
11) a. (-6, 6)
b. (6, -6)
c. When reflecting over the y-axis, keep the y-value the same and take the opposite x-value. When reflecting over the x-axis, keep
the x-value the same and take the opposite y-value.
12)
Preimage
90°
180°
270°
(0, 0)
(0, 0)
(0, 0)
(0, 0)
(0, 2)
(2, 0)
(0, -2)
(-2, 0)
(6, 2)
(2, -6)
(-6, -2)
(-2, 6)
(6, 0)
(0, -6)
(-6, 0)
(0, 6)
For each clockwise 90° rotation about the origin, switch the x and y coordinates and make the y-value the opposite sign.
13) a. ½
b. R”(1, 7); U”(-6, 5); N”(-1, 4)
c. ΔR”U”N” is similar to ΔRUN because it is half the size of ΔRUN. ΔR”U”N” is congruent to ΔR’U’N’ because the translation
does not change the figure’s shape or size.
14) Possible answer: Reflect over the y-axis and translate ( x, y )  ( x  9, y  1) .
Another possibility: Translate ( x, y )  ( x  9, y  1) and reflect over the x-axis.
***There are other possibilities!!!