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Match the reasons with the statements in the proof.
Given: a | | b, m 2 = m 3
Prove: m 1 = m 3
1. a||b, m∠2 = m∠3
Given
2. m∠1 = m∠2
Substitution
3. m∠1 = m∠3
If lines are ||, corresponding angles are equal.

Match the reasons with the statements in the proof Given a b m 2 m 3 Prove m 1 m 3 1 ab m2 m3 Given 2 m1 m2 Substitution 3 m1 m3 If lines are corresponding angl class=

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budwilkins
Given: a | | b, m 2 = m 3
Prove: m 1 = m 3

1. a || b, m∠2 = m∠3
Given

2. m∠1 = m∠2
If lines are ||, corresponding angles are equal.

3. m∠1 = m∠3
Substitution
fichoh

The correct matching of the statement and reasons in the proof given goes thus:

  • a | | b - - - - - - - - - - GIVEN

  • m∠1 = m∠2 - - - - corresponding angles are equal

  • m∠1 = m∠2 - - - - - Substitution

The first reason stated when starting a proof is 'GIVEN' as it has been stated in the question a | | b and m 1 = m 3

From the diagram, the traversal cuts the two parallel lines, creating a corresponding angle at m∠1 and m∠2

Since, we've been told that m1 = m3 in the initial statement, we assign the value of the angle m∠1 to m∠3 (substitution)

Hence, the proof.

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