Questions: In this rug, given the horizontal segments are parallel and angle 1 is congruent to angle 2, prove angle 3 is congruent to angle 5.

Transcript text: In this rug, given the horizontal segments are parallel and $\angle 1 \cong \angle 2$, prove $\angle 3 \cong \angle 5$.

Solution

Step 1: Identify Given Information

Given:

Step 2: Use Corresponding Angles Postulate

Since the horizontal segments are parallel, and the transversal intersects them, the corresponding angles are equal. Therefore:

Step 3: Apply Transitive Property

Since ∠1 ≅ ∠2 (given) and ∠3 ≅ ∠1 (from Step 2), by the transitive property:

∠3 ≅ ∠2

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