6) complete the proof.
given: $ \triangle a b o $ and $ \triangle d e o $ are right $ \delta \mathrm{s} ; \overline{a b} \cong \overline{d e} ; \overline{a b} \| \overline{d e} $.
prove: $ \triangle a b o \cong \triangle d e o $
statements
1. $ \triangle a b o $ and $ \triangle d e o $ are right $ \delta \mathrm{s} $; $ \overline{a b} \cong \overline{d e} ; \overline{a b} \| \overline{d e} $.
2. $ \angle a \cong \angle d $
3. $ \triangle a b o \cong \triangle d e o $
reasons
1. given
2. $ \overline{a d} $ is a transversal cutting parallel segments $ \overline{a b} $ and $ \overline{d e} $.
3.

Question

Accepted Answer

# Explanation:
## Step1: Find reason for ∠A ≅ ∠D
When two parallel lines ($\overline{AB}$ and $\overline{DE}$) are cut by a transversal ($\overline{AD}$), the alternate interior angles are congruent. So the reason for $∠A\cong∠D$ is "Alternate Interior Angles Theorem".
## Step2: Prove $\triangle ABO\cong\triangle DEO$
We have two right triangles ($\triangle ABO$ and $\triangle DEO$), $∠A\cong∠D$ (from step 1), $\overline{AB}\cong\overline{DE}$ (given). By the Angle - Side - Angle (ASA) congruence criterion for right triangles (since the right angles $∠B$ and $∠E$ are also congruent as they are right angles ($90^{\circ}$) and we have a side and two angles),  $\triangle ABO\cong\triangle DEO$.

# Answer:
2. Alternate Interior Angles Theorem; 3. ASA (Angle - Side - Angle)

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QUESTION IMAGE

Question

Explanation:

Step1: Find reason for ∠A ≅ ∠D

Step2: Prove \(\triangle ABO\cong\triangle DEO\)

Answer: