Question

Match the reasons with the statements in the proof.

Given: c | | d, m 4 = m 5
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
Substitution
2. m∠4 = m∠7
Vertical angles are equal.
3. m∠5 = m∠8
If lines ||, alternate interior angles are equal.
4. m∠7 = m∠8
Given

Answer 1

Given: c | | d, m 4 = m 5
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
GIVEN
2. m∠4 = m∠7
If lines ||, alternate interior angles are equal.
3. m∠5 = m∠8
Vertical angles are equal.
4. m∠7 = m∠8
Substitution

Answer 2

Explanation:

Given: c is parallel to d and ∠4=∠5.

To prove: ∠7=∠8

Proof:

Statement Reason

1. c║d, ∠4=∠5 Given

2.∠4=∠7 If lines ||, alternate interior angles are equal.

3.∠5=∠8 Vertical angles are equal

Since, ∠4=∠5, therefore ∠7=∠8

4.∠7=∠8 Substitution