Download Geometry PreAP Homework 9/21 Name: Period: Use this diagram to

Geometry PreAP
Homework 9/21
Name:
Period:
Use this diagram to identify the property, postulate, or theorem that justifies each statement.
1. 𝑃𝑄 + 𝑄𝑅 = 𝑃𝑅
a. Angle addition postulate
b. Addition property
c. Definition of congruent segments
d. Segment addition postulate
̅̅̅̅ ≅ 𝑄𝑅
̅̅̅̅.
̅̅̅̅, then 𝑃𝑄
2. If Q is the midpoint of 𝑃𝑅
a. Definition of a midpoint
b. Definition of congruent segments
c. Definition of a segment bisector
d. Segment addition postulate
3. ∠3 ≅ ∠4
a. Definition of a linear pair
b. Definition of congruent angles
c. Vertical angle theorem
d. Definition of angle bisector
4. If ∠1 is complementary to ∠2, then 𝑚∠1 + 𝑚∠2 = 90
a. Angle addition postulate
b. Addition property of equality
c. Definition of perpendicular
d. Definition of complementary
5. If 𝑚∠3 = 90, then ∠3 is a right angle
a. Definition of perpendicular
b. Definition of complementary angles
c. Definition of right angle
d. Vertical angles are congruent
Write a justification for each step.
Given: ∠1 and ∠2 are supplementary and ∠1 ≅ ∠3.
Prove: ∠3 and ∠2 are supplementary.
Statement
𝟏. ∠1 and ∠2 are supplementary and ∠1 ≅ ∠3.
2. m∠1 + m∠2 = 180°
3. ∠1 ≅ ∠3
4. m∠1 = m∠3
5. m∠3 + m∠2 = 180°
𝟔. ∠3 and ∠2 are supplementary
Justification
Fill in the blanks of these proofs.
Given: ∠2 and ∠3 are supplementary
Prove: 𝑚∠1 = 𝑚∠4
1
3
2
4
1
Statement
1. ∠𝟐 and ∠𝟑 are supplementary
Justification
1. Given
2. ∠𝟑 and ∠𝟒 are supplementary
2.
3. ∠𝟐 ≅ ∠𝟒
3.
4.
4. Vertical Angle Theorem
5.
5. Transitive Property of Congruence
6.
6.
̅̅̅̅ ⊥ 𝐵𝐷
̅̅̅̅ and ∠1 and ∠2 are complementary
Given: 𝐴𝐵
Prove: ∠1 ≅ ∠3
A
E
C
3
B
2
D
F1
Statement
1. ̅̅̅̅
𝑨𝑩 ⊥ ̅̅̅̅̅
𝑩𝑫
∠𝟏 and ∠𝟐 are complementary
2.
Justification
1.
3.
3. Definition of Right Angles
4. 𝒎∠𝟐 + 𝒎∠𝟑 = 𝒎∠𝑨𝑩𝑫
4.
5.
5. Substitution
6.
6.
7. ∠𝟏 ≅ ∠𝟑
7.
Create a two-column proof.
2. Definition of Perpendicular lines
G
Given: ∠1 and ∠2 are supplementary,
∠3 and ∠4 are supplementary,
∠2 ≅ ∠3
Prove: ∠1 ≅ ∠4
Statement
1.
Justification
1.
2.
2.
Justification Word Bank:
Segment Addition Postulate
Angle Addition Postulate
Definition of Congruent Angles
Definition of Congruent Segments
Definition of Midpoint
Definition of Angle Bisector
Definition of Segment Bisector
Linear Pair Theorem
Definition of Supplementary Angles
Definition of Complementary Angles
Congruent Complements Theorem
Congruent Supplements Theorem
Right Angles Congruence Theorem
Definition of Perpendicular