MTIII
Name ________________________
Unit 2c Review
1.) In the figure at the right, quadrilateral ABCD is similar to quadrilateral EFGH.
a. Write four equal ratios to show corresponding sides are proportional.
___________ ___________ ___________ ___________
b. Find HG.
HG =___________
c. The sum of the measures of <A and <C equals the sum of the measure
of which two angles of quadrilateral EFGH?
Angles:_________
d. Find the scale factor.
Scale: __________
2.) Two similar polygons are shown. Find the values of x and y.
a.
b.
x=_______ y=_______
x=_______ y=_______
3.) Use a proportion to solve each problem.
a. On a map, the distance between two cities is nine inches. On the map, three inches represents 20 miles.
What is the actual distance between the cities?
Distance=__________
b. The ratio of seniors to juniors in the Math Club is 2:3. If there are 21 juniors, how many seniors are in
the club?
# of seniors=__________
4.) Suppose the measure of corresponding sides of ∆ABC and ∆DEF are proportional.
a. If BC = 24, EF = 9, AC = y + 30, and DF = y, find AC.
AC=__________
b. If AB = 5x + 3, BC = 2, DE = 4, and EF = 1, find x.
x=__________
5.) Solve each proportion using cross products.
a.
b.
x=_______
x=_______
AC CE

6.) In the figure,
. Use proportions to complete the table.
CD CB
AC BC AB CE ED DC
10
4
8
c.
r=_______
6.) Identify the similar triangles in each figure. Explain why they are similar and find the missing
measures x and y.
a.
b.
x=_______ y=_______
x=_______ y=_______
7.) Use the given information to determine whether each pair of triangles is similar. Justify your answer.
a.
b.
c.
_______________
_______________
_______________
8.) Identify the similar triangles in each figure. Explain why they are similar and find the missing
measures.
If MN ║ AB, find AB, BC, and BN.
AB=_______
BC=_______
BN=_______
9.) In ∆XYZ, determine whether it is always true that AB ║ YZ under the given conditions.
XA = 6, AY = 4, XB = 8, and BZ = 5
_______________
10.) Find the value of x.
a.
x=_______
b.
x=_______
11.) Using the figure at the right, determine the value of x that would make DE ║ CB under each set of
conditions.
AC = 30, AD = 10
AE = 22, EB = x + 4
x=_______
12.) Using the figure at the right, determine the value of x and if JG ║ RQ and find RQ.
PJ = 6, JG = 5, PG = 4, GQ = 4, RQ = x + 6, JR = 6
x=_______ RQ = _______
*All symbols that look like a division sign are really plus (+) signs*
17.) Prove the midsegment theorem:
Triangle ABC has vertices at points: A(10,9), B(4,1), and C(-2,-7)
a) Find the coordinates of the midpoint of AB (D) and BC (E).
b) Show that AC is parallel to DE.
c) Show 2DE = AC.