Geometry Exam 3 Review
1. Circle the triangles that can be proven to be congruent and state how you know they are congruent.
a.
b.
c.
d.
2. True or false (To be true, it must always be true):
a. If two angles share a common vertex, then they must be adjacent angles.
b. If a quadrilateral has all four angles congruent, then the quadrilateral must be a square.
c. If two lines cut by a transversal form a pair of supplementary interior angles on the same side of
the transversal, then the lines must be parallel.
d. If two sides and any one angle of one triangle are congruent to two sides and any one side of
another triangle, then the triangles must be congruent.
3.
B
C
R
A
Given: isosceles trapezoid ABCD, isosceles triangles BRC and ARD
If  BRA  80 and < BCD = 100 find the measures of < CDA and < BAR
D
4. Use a compass and straight edge to construct a 60 degree angle.
5. Use a compass and straight edge to construct a 45 degree angle.
6. Use a compass and a straight edge to construct a right isosceles triangle with legs of length a.
a
7. Use a compass and straight edge to construct a triangle given two sides of lengths a and b, and their
included angle C. (Note: you must reconstruct angle C.)
a
b
C
8.
1 2 3
4 5 6
Given: the figure
<7 = 100 
<9 = 50 
7 8
11 12
9 10
13 14
a. Name a pair of vertical angles ___________________________________
b. Name a pair of corresponding angles______________________________
c. Name a pair of alternate interior angles_____________________________
d. Name a pair of alternate exterior angles_____________________________
e. Name a pair of interior angles on the same side of the transversal______________________
f. Name a pair of exterior angles on the same side of the transversal______________________
g. <4 = _______________________
h. <8 = ________________________
i.
<12 =_______________________
j.
<3 = ________________________
k. < 6 = ________________________
l.
< 5 = ________________________
m. < 2 = ________________________
9.
A
B
C
In  ACD, AD  CD ,  ADB   CDB ,
AC=16 cm, AD = 20 cm and  ADB = 24
Round to the nearest hundredth if needed.
a. How long is BC ?
D
b. How long is BD ?
c. What is the measure of  DAB
10. Given isosceles trapezoid ABCD with AB  CD , prove that ABD  DCA
B
C
A
D
11. A
B
Given that C is the midpoint of both AE and BD , prove that  A   E
C
D
E
12. Find the measures of all of the angles of the following parallelogram.
2x+25
x  10
13.
Use the given figure to calculate the numbered
angles given that m n
1 2 45 
3
m
n
5
70  4
6
14.
B
20m
C
30 
In the parallelogram ABCD, find the height.
Then calculate the area of ABCD.
18 m
A
D
Answers: 1.a. not  1.b.  by SSS or SAS 1.c.  by HA, AAS or ASA 1.d. not  2.a. False 2.b. False
2.c. True 2.d. False 3. CDA = 80, BAR = 40 4. - 7. See below 8.a. through f. more than one answer
is possible. Example answers are given. 8.a. 1 and 6 8.b. 6 and 14 8.c. 6 and 9 8.d. 3 and 11
8.e. 6 and 10 8.f. 1 and 13 8.g. 80  8.h.80  8.i. 100  8.j.80  8.k.50  8.l.50  8.m. 50 
9.a. 8 cm 9.b. 18.33 cm 9.c. 66 
10. Statement
Reason
11. Statement
Reason
1. AB  CD
1. Given
1.C is midpoint of AE and BD
1. Given
2. BAD  CDA
2. Given
2. AC  EC and DC  BC
2. Def. of midpoint
3. AD  AD
4. ABD   DCA
3. Reflexive
4. SAS
3. ACD  ECB
4. ACD   ECB
5. A  E
3. Vertical angles
4. SAS
5. CP
12. two angles are 45  and two angles are 135 
2
13. 1  70, 2  65, 3  65, 4=110, 5=135, 6=55 14. Height = 9m Area = 180 m