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Geometry
Unit 5: Worksheet 19
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Date: ___________________ Pd: ______
Final Proof Practice
1.
Given:
Prove:
A
B
C
P
Q
R
Statements
Reasons
1.
1. Given
2.
3.
2. Addition Property of Equality
3. Segment Addition Postulate
4.
4. Substitution Property of Equality
5.
5. If two segments have equal measure, then they are
congruent.
2.
Given:
M
A
Prove:
D
P
B
N
C
Statements
O
Reasons
1.
1. Given
2.
3.
2. If 2 angles are congruent, then they have equal
measure.
3. Addition Property of Equality
4.
4. Angle Addition Postulate
5.
6.
5. Substitution Property of Equality
6. If two angles have equal measure, then they are
congruent.
3.
Given:
Prove:
X
Y
Z
Statements
T
Reasons
1.
2.
3.
1. Given
2. Reflexive Property of Equality
3. Subtraction Property of Equality
4.
4. Segment Subtraction Postulate
5.
5. Substitution Property of Equality
E
4.
Given:
Prove:
A
B
C
D
F
Statements
Reasons
1.
2.
1. Given
2. Definition of Linear Pair.
3.
3. If 2 angles form a linear pair, then they are
supplementary.
4. If 2 angles are supplementary to congruent angles,
then they are congruent.
4.
5.
B
Given:
Prove:
A
Statements
E
F
C
D
Reasons
2.
3.
1. Given
2. Reflexive Property of Equality
3. Addition Property of Equality
4.
4. Segment Addition Postulate
5.
5. Substitution Property of Equality
6.
6. If two segments have equal measure, then they are
congruent.
1.
6.
Given:
Prove:
2
1
Statements
3
4
Reasons
1.
2.
1. Given
2. Definition of Linear Pair.
3.
3. If 2 angles form a linear pair, then they are
supplementary.
4. If 2 angles are supplementary to congruent angles, then
they are congruent.
4.
7.
A
Given:
E
bisects
D
Prove:
F
G
Statements
B
C
Reasons
1. Given
1.
bisects
2. If an angle is bisected, it is divided into 2 congruent
angles.
3. If two angles are congruent to the same angle, then
they are congruent.
OR Transitive Property of Congruence
2.
3.
A
C
8.
Given:
Prove:
D
B
Statements
E
Reasons
1.
1. Given
2.
3.
2. If 2 angles are congruent, then they have equal
measure.
3. Reflexive Property of Equality
4.
4. Subtraction Property of Equality
5.
5. Angle Subtraction Postulate
6.
7.
6. Substitution Property of Equality
7. If 2 angles have equal measures, then they are
congruent.
9.
Given:
Prove:
3
2
4
1
Statements
Reasons
1. Given
2. If 2 angles have equal measures, then they are
congruent.
3. Definition of Vertical Angles
1.
2.
3.
4.
4. If 2 angles are vertical angles, then they are
congruent.
5.
5. If 2 angles are congruent to congruent angles,
then they are congruent to each other.
OR Transitive Property of Congruence
6. If 2 angles are congruent, then they have equal
measures.
6.
G
10. Given:
H
R
Prove:
X
Statements
Q
Reasons
1.
1. Given
2.
2. If 2 rays are perpendicular, then they form right
angles.
3. If 2 angles form a right angle, then they are
complementary
4. If 2 angles are complementary to the same
angle, then they are congruent.
3.
4.
11. Given:
Prove:
1
Statements
1.
2.
3.
4.
3
4
2
Reasons
1. Given
2. Definition of Linear Pair
3. If 2 angles form a linear pair, then they are
supplementary.
4. If 2 angles are supplementary to congruent
angles, then they are congruent.
E
D
12. Given:
Prove:
C
2
1
3
A
B
F
Statements
Reasons
1.
2.
1) Given
2) Definition of Vertical Angles
3.
3) If 2 angles are vertical angles, then they are
congruent.
4) If two angles are congruent to the same angle,
then they are congruent to each other.
OR Transitive Property of Congruence
4.
OR
Statements
1.
2.
3.
are corresponding angles
4.
5.
are alternate interior angles
Reasons
1. Given
2. Definition of Corresponding Angles
3. If 2 lines are cut by a transversal and
corresponding angles are congruent, then the lines
are parallel.
2. Definition of Alternate Interior Angles
3. If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
d
13. Given:
b
Prove:
w
1
3
4
2
Statements
1.
2.
3.
4.
are same-side interior angles
5.
6.
are alternate exterior angles
6
5
Reasons
1. Given
2. If the measures of two angles sum to 180˚, then
the angles are supplementary.
3. Definition of Same-Side Interior Angles
4. If 2 lines are cut by a transversal and same-side
interior angles are supplementary, then the lines
are parallel.
5. Definition of Alternate Exterior Angles
4. If 2 lines are cut by a transversal, then alternate
exterior angles are congruent.
q
p
14. Given: b || c
b
Prove: p || q
c
Statements
1.
2.
3.
3
2
Reasons
1. Given
are corresponding angles
4.
5.
6.
4
1
are corresponding angles
2. Definition of Corresponding Angles
3. If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
4. If 2 angles are congruent to the same angle,
then they are congruent.
OR Transitive Property of Congruence
5. Definition of Corresponding Angles
6. If two lines are cut by a transversal and
corresponding angles are congruent, then the lines
are parallel.
OR
Statements
1.
2.
3.
are alternate interior angles
4.
5.
6.
Reasons
1. Given
are alternate interior angles
2. Definition of Alternate Interior Angles
3. If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
4. If 2 angles are congruent to the same angle,
then they are congruent.
OR Transitive Property of Congruence
5. Definition of Alternate Interior Angles
6. If two lines are cut by a transversal and
alternate interior angles are congruent, then the
lines are parallel.
d
15. Given:
Prove:
b
w
1
3
4
2
Statements
1.
2.
3.
5
Reasons
1. Given
are alternate interior angles
4.
5.
6.
6
form a linear pair
are supplementary
7.
8.
2. Definition of Alternate Interior Angles
3. If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
4. If two angles are congruent, then they have
equal measures.
5. Definition of Linear Pair
6. If 2 angles form a linear pair, then they are
supplementary.
7. If 2 angles are supplementary, then their
measures add to 180˚.
8. Substitution Property of Equality
y
16. Given: d  y
k y
Prove: k|| d
1
2
3
4
q
k
Statements
d
Reasons
1.
1. Given
2.
2. If 2 lines are perpendicular to the same line,
then they are parallel to each other.