Proofs About Angles Practice

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Question
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A horizontal line is intersected by two parallel lines lower s and lower t that slant from right to left forming eight angles.

Clancy wrote a proof to prove that alternate interior angles are congruent.

Statement Reason
1. m∠E=m∠H
Vertical Angles Theorem
2. Corresponding Angles Postulate
3. m∠E=m∠D
Transitive Property of Equality
4. ∠E≅∠D
definition of congruence

What is the missing statement in his proof?

Option 1: m∠E=m∠A

Option 2: m∠C=m∠G

Option 3: m∠D=m∠H

(1 point)
The missing statement is Option
.

Answer 1

To find the missing statement in Clancy's proof regarding alternate interior angles, we need to consider the geometry involved with the parallel lines and the transversal.

We know:

1. \( m∠E = m∠H \) (from the Vertical Angles Theorem)
2. The missing statement should logically relate \( m∠H \) with either \( m∠A \), \( m∠C \), or \( m∠D \).
3. From \( m∠H \) being equal to \( m∠D \) (since \( m∠D \) is an alternate interior angle to \( m∠E \)), we can conclude that \( m∠D = m∠H \) must be true.

Therefore, looking at the provided options:

• Option 1 \( m∠E = m∠A \) does not relate directly to \( m∠H \).
• Option 2 \( m∠C = m∠G \) does not involve the angles needed here.
• Option 3 \( m∠D = m∠H \) logically follows from \( m∠E = m∠H \) through the properties of corresponding and alternate angles.

So the missing statement must be:

The missing statement is Option 3: m∠D=m∠H.