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HS Mathematics III – Geometry
Session 2 Evaluation
Do not write anything on the questionnaire. Use pad paper.
A. Write TRUE if the statement is always true. Otherwise, change the underlined word/phrase/symbol/numeral to make the
statement true.
1. The measure of a/an right angle is exactly 90.
2. The measure of an obtuse angle is greater than 90 but less than 360.
3. An angle is the union of two noncollinear rays that have the same vertex.
4. Two perpendicular lines form four congruent angles.
5. Two angles are supplementary if the sum of their measures is 180.
6. If two angles are supplementary, then they form a linear pair.
7. If two angles form a linear pair, then they are supplementary.
8. If the measures of two angles are congruent, then their supplements are congruent.
9. If two congruent angles form a linear pair, then both of them are acute angles.
10. All right angles are congruent.
11. The sides of adjacent angles form two pairs of opposite rays.
12. The point of intersection of two vertical angles is the endpoint of each angle.
13. The set of points in the interior of an angle is a convex set.
14. If  A is supplementary to  B and  C is supplementary to  B, then  A is congruent to  C.
15. If two angles are congruent, then their sides are equal.
B. Make an illustration for each of the following. Label your drawings accordingly.
1. Angle T
3. Angle 2
2. Angle BOX
4. Angle y
C. Use the figure at the right in answering the following items.
1. Name three angles.
2. What is the side common to  BAC and  CAD?
3. Name all points in the interior of  BAD.
4. Name all points in the interior of  CAD.
5. Name all points in the interior of  BAC.
C
B
E
F
A
D
D. Illustrate separately each of the following and:
1. name two angles having a common vertex but not having a common side.
2. name two angles that are adjacent but not supplementary.
3. name two angles that are adjacent and supplementary.
E. Show complete solutions and box final answers. Round off to two decimal places.
1. Two vertical angles,  a and  b, are supplementary. Find their measures.
2. If m  c = x – 5 and m  d = 4x – 30, what value of x will make the two angles complementary?
3. If m  LOR = 44 –n, find the measure of its complement.
4. If m  e + m  f = 360 and 4(m  e) = m  f, what is m  e?
1
Year, Section and CN: _______________
Name: ______________________________________________
F. Complete the following two-column proofs by supplying the missing statements and/or reasons.
a. Given: F is the midpoint of AC
Z is the midpoint of CY
AZ  ZY
A
Y
F
Z
Prove: FC  CZ
Statements
1. F is the midpoint of AC , Z is the midpoint of CY
and AZ  ZY
2. AF = FC and ZY = CZ
3. AF = ZY
4. AF = FC and AF = CZ
5. FC = CZ
6. FC  CZ
C
Reasons
1.
2.
3.
4.
5.
6.
b. Given:  CRY   ERB
Prove:  CRB   ERY
Y
B
C
E
Statements
1.  CRY   ERB
2.
3. m  YRB = m  YRB
4. m  CRY + m  YRB = m  ERB + m  YRB
5. m  CRY + m  YRB = m  CRB
6.
7. m  CRB = m  ERY
8.  CRB   ERY
Reasons
1.
2. Definition of Congruence
3.
4.
5.
6. Angle Addition Postulate
7.
8.
c. Given:  1 and  2 form a linear pair
 3 and  4 form a linear pair
2 4
Prove:  1   3
Statements
1.
2.
1
2
3
4
Reasons
1. Given
2. Supplement Postulate and Definition of
Supplementary Angles
2
3.
4.
5. m  1 + m  2 = m  3 + m  4
6.
7.
8. m  1 + m  2 = m  3 + m  2
9.
10.
3. Given
4. Supplement Postulate and Definition of
Supplementary Angles
5.
6. Given
7. Definition of Congruence
8.
9. Addition Property of Equality
10. Definition of Congruence
d. Given: AB  BC
 DCB is complementary to  DBC
A
Prove:  DCB   ABD
D
B
Statements
1. AB  BC
2.
3.
4.
5. m  ABD + m  DBC = m  ABC
6. m  ABD + m  DBC = 90
7.
8. m  DCB = m  ABD
9.
C
Reasons
1.
2. Definition of Perpendicular and Definition of Right
Angle
3. Given
4. Definition of Complementary Angles
5.
6.
7. Transitive and Symmetric Properties of Equality
8.
9. Definition of Congruence
e. Given:  DBF   ECG
A
Prove:  ABC   ACB
D
B
F
Statements
C
E
G
Reasons
3
4