Question

question 1 (multiple choice worth 1 points) (03.03r mc) if ( mangle abc = 45^circ ) and ( mangle ecd = 45^circ ), which statement explains whether the aa similarity postulate can be used to determine whether ( \triangle bac sim \triangle edc )?
yes, the aa similarity postulate can be used because a reflection over line ( l ) will establish that ( overline{ab} cong overline{de} ).
yes, the aa similarity postulate can be used because a reflection over line ( l ) will establish that ( angle abc cong angle dec ).
no, the aa similarity postulate cannot be used because a reflection over line ( l ) will establish that ( overline{ab} ) and ( overline{de} ) are not congruent.
no, the aa similarity postulate cannot be used because a reflection over line ( l ) will establish that ( angle abc ) and ( angle dec ) are not congruent.
question 2 (multiple choice worth 1 points)

Explanation:

To determine if \(\triangle BAC\sim\triangle EDC\) using the AA (Angle - Angle) similarity postulate, we need two pairs of congruent angles. We know that \(\angle A=\angle D = 90^{\circ}\) (right angles). A reflection over line \(f\) will map \(\angle ABC\) to \(\angle DEC\) (since \(m\angle ABC=m\angle ECD = 45^{\circ}\), and the reflection will preserve the angle measure). So, we have two pairs of congruent angles (\(\angle A\cong\angle D\) and \(\angle ABC\cong\angle DEC\)) which is required for the AA similarity postulate.

Answer:

Yes, the AA similarity postulate can be used because a reflection over line \(f\) will establish that \(\angle ABC\cong\angle DEC\).