Geometry Test chapters 3-4
Geometry Test Chapters 3 and 4 Name ____________________________________
1. __________________ angles are angles with measures that add to equal 90.
2. Vertical angles are a pair of _____________________ angles formed by two intersecting lines.
3. In the figure below FOG and GOH are complementary. If m FOG = 2X + 10 and m GOH = 2X, find X.
4. Use the definition of an angle bisector to answer the question below:
If PQ bisects SPF, and if m 
SPQ = 3X – 2, and m QPF = 2X + 9 then find m SPF.
Is SPF acute, right or obtuse?
From each statement below, tell the definition, property, postulate, or theorem that justifies the prove statement:
5. Given m PST + m LQR = 90
and m DEF = m LQR:
Prove: m PST+ m DEF = 90
6. Given : 1 and 2 are supplements of 3; Prove 1 = 2
Tell whether each of the angles below is adjacent.
If a pair is not adjacent, briefly tell why not.
7. TPU and UOV
8. UOV and VOW
9. Find the measure of all the angles
JOK
JOM
LOM
KOL
10. Find the measure of HKL below
Find the measures of the complement and supplement of each angle below:
11. mUHJ = 21
Complement =
Supplement =
12. m LPW = 90-2x
Complement
Supplement
13. Match the angles:
____ adjacent angles
____vertical angles
____alternate interior angles
____alternate exterior angles
____corresponding angles
____supplementary angles
Find the measure of each angle below
14. LNO
15. KLN
Write and equation to represent each question; then solve the equation to get your answer. 16. A supplement of an angle is twice as large as the angle. Find the measure of the angle.
17. The difference between the measures of 2 supplementary angles is 42. Find both angles.
Tell whether each definition below passes the reversibility test by writing its converse and determining
whether the converse is true.
18. If two angles are a linear pair, then the sum of their measures is 180.
19. Parallel lines are lines that lie in the same plane and never intersect.
From each given statement below, tell the definition, property, postulate, or theorem that justifies each prove statement:
20. Given AB is parallel to CD; prove 3 and 6 are supplementary
21. Given 3 = 5; prove AB is parallel to CD
Complete each sentence with always, sometimes, or never
22. Corresponding angles are ____________________ congruent.
23. If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are
___________________ supplementary.
BONUS BONUS BONUS BONUS BONUS BONUS EXTRA CREDIT - one point for each blank filled in correctly.
Complete the proof below by filling in the blanks:
Given:
DE EF
DFE is complementary to DEG
Prove: DF GH
Statements Reasons:
1. DE EF 1.
2. 2. Given
3. 3. Definition of a right angle.
4. m DEG + mDEF + m FEH = 180 4. A straight angle measures 180
5. m DEG + 90 + m FEH = 180 5.
6. m DEG + mFEH = 90 6.
7. 7.Definition of complementary angles
8. FEH = DFE 8.
9. 9. If two lines form congruent alternate interior angles with a transversal, then the lines are parallel
SPQ = 3X – 2, and m QPF = 2X + 9 then find m SPF.
Is SPF acute, right or obtuse?
From each statement below, tell the definition, property, postulate, or theorem that justifies the prove statement:
5. Given m PST + m LQR = 90 and m DEF = m LQR:
Prove: m PST+ m DEF = 90
6. Given : 1 and 2 are supplements of 3; Prove 1 = 2
Tell whether each of the angles below is adjacent.
If a pair is not adjacent, briefly tell why not.
7. TPU and UOV
8. UOV and VOW
9. Find the measure of all the angles
JOK
JOM
LOM
KOL
10. Find the measure of HKL below
Find the measures of the complement and supplement of each angle below:
11. mUHJ = 21
Complement =
Supplement =
12. m LPW = 90-2x
Complement
Supplement
13. Match the angles:
____ adjacent angles
____vertical angles
____alternate interior angles
____alternate exterior angles
____corresponding angles
____supplementary angles
Find the measure of each angle below
14. LNO
15. KLN
Write and equation to represent each question; then solve the equation to get your answer. 16. A supplement of an angle is twice as large as the angle. Find the measure of the angle.
17. The difference between the measures of 2 supplementary angles is 42. Find both angles.
Tell whether each definition below passes the reversibility test by writing its converse and determining
whether the converse is true.
18. If two angles are a linear pair, then the sum of their measures is 180.
19. Parallel lines are lines that lie in the same plane and never intersect.
From each given statement below, tell the definition, property, postulate, or theorem that justifies each prove statement:
20. Given AB is parallel to CD; prove 3 and 6 are supplementary
21. Given 3 = 5; prove AB is parallel to CD
Complete each sentence with always, sometimes, or never
22. Corresponding angles are ____________________ congruent.
23. If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are
___________________ supplementary.
BONUS BONUS BONUS BONUS BONUS BONUS EXTRA CREDIT - one point for each blank filled in correctly.
Complete the proof below by filling in the blanks:
Given:
DE EF
DFE is complementary to DEG
Prove: DF GH
Statements Reasons:
1. DE EF 1.
2. 2. Given
3. 3. Definition of a right angle.
4. m DEG + mDEF + m FEH = 180 4. A straight angle measures 180
5. m DEG + 90 + m FEH = 180 5.
6. m DEG + mFEH = 90 6.
7. 7.Definition of complementary angles
8. FEH = DFE 8.
9. 9. If two lines form congruent alternate interior angles with a transversal, then the lines are parallel