Download File - LSL Math Weebly

Math 20-2
Chapter 2 Properties of Angles and Triangles
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Which pairs of angles are equal in this diagram?
a.
b.
c.
d.
b = c, e = g, and f = h
b = f, c = g, and d = h
b = e, c = h, and d = g
b = a, c = e, and d = f
2. In which diagram(s) is AB parallel to CD?
1.
a.
b.
c.
d.
2.
Choice 1 only
Choice 2 only
Choice 1 and Choice 2
Neither Choice 1 nor Choice 2
3. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
e = 130°
f = 62°
c = 50°
b = 50°
4. Which angle property proves DAB = 120°?
a.
b.
c.
d.
alternate exterior angles
corresponding angles
vertically opposite angles
alternate interior angles
5. Which angle property proves EFS = 28°?
a. alternate exterior angles
b. supplementary angles
c. alternate interior angles
d. corresponding angles
6. Which are the correct measures of the indicated
angles?
a.
b.
c.
d.
w = 77°, x =103°, y = 103°
w = 77°, x =77°, y = 103°
w = 103°, x =103°, y = 77°
w = 103°, x =77°, y = 77°
7. Which are the correct measures for DCE and
CAB?
a. DCE = 31°, CAB = 134°
b. DCE = 47°, CAB = 109°
c. DCE = 13°, CAB = 143°
d. DCE = 37°, CAB = 119°

8. Which are the correct measures for OJK, JKO,
and JOK?
11. With which of the following polygons could you
create a tiling pattern?
Choose the best answer.
a.
b.
c.
d.
a square
an equilateral triangle
a rectangle
all of the above
12. With which of the following polygons could you
create a tiling pattern?
a.
b.
c.
d.
OJK = 117°, JKO = 28°, and JOK = 35°
OJK = 117°, JKO = 36°, and JOK = 37°
OJK = 152°, JKO = 18°, and JOK = 10°
OJK = 102°, JKO = 28°, and JOK = 50°
9. Which are the correct measures of the interior
angles of CDE?
a.
b.
c.
d.
a regular octagon
a regular pentagon
a regular hexagon
none of the above
13. The sum of the measures of the interior angles of a
convex polygon is S.
Which expression results in the number of sides of
the polygons?
a.
b. 180°(S – 2)
c.
d.
a.
b.
c.
d.
DCE = 48°, CDE = 75°, and CED = 57°
DCE = 37°, CDE = 86°, and CED = 57°
DCE = 57°, CDE = 86°, and CED = 37°
DCE = 37°, CDE = 68°, and CED = 75°
14. Determine the value of c.
10. Determine the sum of the measures of the interior
angles of this polygon.
a.
b.
c.
d.
1620°
1080°
1260°
1440°
a.
b.
c.
d.
45°
72°
54°
48°
15. State the corresponding sides and angles in this pair
of congruent triangles.
a.
b.
c.
d.
AB  RS, AC  RT, AR
AB  RT, AC  RS, AT
BC  RS, AC  ST, AS
None of the above choices are correct.
16. What can you deduce from the statement ABC 
DFE?
a.
b.
c.
d.
118.What additional piece of information would allow you
to conclude that these triangles are congruent?
a.
b.
c.
d.
A = D and C = F
B = E
AC = DF
all of the above
19. Which angle is equal to D?
C = D
B = D
A = F
none of the above
17. What additional piece of information would allow
you to conclude that these triangles are congruent?
a.
b.
c.
d.
A
B
C
none of the above
20. Which angle is equal to F?
a.
b.
c.
d.
AC = DF
C = F
AB = EF
all of the above
a.
b.
c.
d.
A
B
C
none of the above
Short Answer
21. Determine the measure of PQR.
23. Given QP || MR, determine the measure of MOQ.
24. Can you prove these triangles are congruent? If so,
how?
22. Determine the measure of NMO.
Problem
25. Prove that a triangle cannot contain two right
angles.
26. Is quadrilateral MATH a parallelogram? Explain.
27. Determine the length of DE. Show your reasoning.
Math 20-2
Chapter 2 Properties of Angles and Triangles - Answer Section
MULTIPLE CHOICE
1.
5.
9.
13.
17.
ANS:
ANS:
ANS:
ANS:
ANS:
B
A
B
A
A
2.ANS B
6.ANS:D
10.ANS:A
14.ANS:C
18.ANS: D
3.ANS:D
7.ANS:D
11.ANS:D
15.ANS:A
19.ANS:B
4.ANS:C
8.ANS:A
12.ANS:C
16.ANS:D
20.ANS:C
SHORT ANSWER
21. ANS:
PQR = 122°
22. ANS:
NMO = 82°
23. ANS:
MOQ = 82°
24. ANS:
Yes, by SSS.
PROBLEM
25. ANS:
For example, assume that ABC does contain two right angles, A, and B.


A + B + C = 180°
Sum of angles in triangle is 180°
90° + 90° + C = 180°
Substitute known values.

C = 180° – 90° – 90° Determine C.

C = 0°
This result is not possible, since C must be greater than 0°. Therefore, a triangle cannot contain two right angles.
26. ANS:
It is not a parallelogram. AMT does not equal MTH, so alternate interior angles are not equal.
KEY: angles| triangles
27. ANS:
AB = BC

A = DBC
 ABE = C
ABE  BCD
BE = 10
BD = 15
DE = 5
Given sides
Given angles
Given angles
ASA
Corresponding sides with CD
Corresponding sides with AE
15 – 10 = 5