Question

question 6
10 pts
g.gsr.3.4 (mc)
we are given and
∠bca ≅ ∠eda because they are both
right angles. what else are we able to
prove in order to prove these triangles are
congruent using asa?
image of triangles with right angles and marked sides
○ ∠abc ≅ ∠aed because they alternate
interior angles.
○ because they are corresponding
sides
○ ∠bac ≅ ∠ead because they are
vertical angles.
○ because they are parallel.

Explanation:

To prove triangles congruent by ASA (Angle - Side - Angle), we need two angles and the included side to be congruent. We already know that \(\angle BCA\cong\angle EDA\) (right angles). We also see that \(BA = AE\) (marked with congruency ticks). For ASA, we need another pair of angles that are congruent and include the side \(BA = AE\).

• Let's analyze the vertical angles: \(\angle BAC\) and \(\angle EAD\) are vertical angles. Vertical angles are always congruent. If we can show \(\angle BAC\cong\angle EAD\), along with \(\angle BCA\cong\angle EDA\) and \(BA = AE\) (the included side between the angles), we can use ASA.
• The first option says \(\angle ABC\cong\angle AED\) as alternate interior angles, but there is no information to suggest that the lines are parallel to form alternate interior angles.
• The second option (about corresponding sides) is not relevant for ASA as ASA requires angles and an included side, and this option is not properly stated.
• The fourth option (about sides being parallel) is not relevant to the ASA criterion for triangle congruence.

So the correct reasoning is that \(\angle BAC\cong\angle EAD\) because they are vertical angles.

Answer:

\(\boldsymbol{\angle BAC \cong \angle EAD}\) because they are vertical angles. (The option with this statement)