Deck 1: Line and Angle Relationships

Question 1

Prove: Any two right angles are congruent.
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Use the following drawing. Provide all statements and reasons.
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Given: Right angles 1 and 2
Prove:

Answer 1

S1. Right angles 1 and 2
R1. Given
S2. and R2. The measure of a right angle is 90.
S3. R3. Substitution Property of Equality
S4. R4. Definition of congruent angles.

Question 2

Provide missing statements and reasons for the following proof.
Given: bisects Prove: S1. R1. Given
S2. R2.
S3. R3. Angle-Addition Postulate
S4. R4.
or

Answer 2

S1. Given
R2. Definition of angle-bisector
S3. S4. R4. Substitution Property of Equality

Question 3

Given: Prove: Provide the missing reasons for this proof:
S1. R1.
S2. R2.
S3. R3.
S4. R4.
S5. R5.

Answer 3

R1. Given
R2. Distributive Law
R3. Substitution Property of Equality
R4. Addition Property of Equality
R5. Division (or Multiplication) Prop. of Eq.

Question 4

Given: A-B-C-D as shown
Prove: Supply missing statements and missing reasons for this proof:
S1. R1.
S2. R2.
S3. R3. Segment-Addition Postulate
S4. R4. Substitution Property of Equality

Question 5

Given: In , ; is a right angle.
Prove: and are complementary.
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Provide all statements and reasons for this proof.

Question 6

Given: Prove: Provide the statements for this proof.
S1. R1. Given
S2. R2. Distributive Law (FOIL)
S3. R3. Substitution Proerty of Equality
S4. R4. Addition Property of Equality

Question 7

Given: and are supplementary
Prove: Supply missing statements and missing reasons for this proof.
S1. and are supplementary R1.
S2. R2. If the exterior sides of 2 adjacent angles form a
straight line, the angles are supplementary.
S3. R3. Two angles that are supplementray to the same
angle are congruent.

Question 8

Supply all statements and reasons in the following proof.
Given: is a right angle.
Prove: and are complementary.

Question 9

Given: Prove: Supply all statements and reasons for the proof.

Question 10

Given: is a right angle
Prove: and are complementary
Supply missing statements and missing reasons for this proof.
S1. R1. Given
S2. R2.
S3. R3. Angle-Addition Postulate
S4. R4.
S5. R5.

Question 11

Given: is complementary to ; is complementary to (no drawing provided)
Prove: ​
Supply missing reasons for this proof.
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S1. is complementary to R1.
S2. is complementary to R2.
S3. R3.
S4. R4.
S5. R5.
S6. R6.
S7, R7.

Question 12

In the figure, A-B-C. Explain why and must be supplementary.

Question 13

Supply missing statements and reasons for the following proof.
Given: and intersect at point X
Prove: S1. R1.
S2. and are supp. R2.
S3. R3. If the exterior sides of two adjacent angles form a
straight line, these angles are supplementary.
S4. R4. Two angles that are supplementary to the same
angle are congruent.