question 5 (multiple choice worth 1 points) (03.03r mc) if ( mangle abc = 53^circ ) and ( mangle ecd = 37^circ ), which statement explains whether the aa similarity postulate can be used to determine whether ( riangle bac sim riangle edc )? yes, the aa similarity postulate can be used because a reflection over line l will establish that ( angle abc cong angle dec ) yes, the aa similarity postulate can be used because a reflection over line l will establish that ( overline{ab} cong overline{de} ) 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. 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.

Question

question 5 (multiple choice worth 1 points) (03.03r mc) if ( mangle abc = 53^circ ) and ( mangle ecd = 37^circ ), which statement explains whether the aa similarity postulate can be used to determine whether ( 	riangle bac sim 	riangle edc )? yes, the aa similarity postulate can be used because a reflection over line l will establish that ( angle abc cong angle dec ) yes, the aa similarity postulate can be used because a reflection over line l will establish that ( overline{ab} cong overline{de} ) 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. 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.

Accepted Answer

# Brief Explanations:
1. First, analyze the right triangles $ \triangle BAC $ and $ \triangle EDC $. Both are right triangles ( $ \angle A = \angle D = 90^\circ $ ).
2. For $ \triangle BAC $, since $ \angle A = 90^\circ $ and $ m\angle ABC = 53^\circ $, then $ m\angle BCA=180^\circ - 90^\circ - 53^\circ = 37^\circ $.
3. Given $ m\angle ECD = 37^\circ $, and by reflection over line $ l $, $ \angle BCA \cong \angle ECD $, and we can also check the other angles. Also, $ \angle ABC $: in $ \triangle BAC $, $ \angle ABC = 53^\circ $, in $ \triangle EDC $, $ \angle DEC=180^\circ - 90^\circ - 37^\circ = 53^\circ $, so $ \angle ABC \cong \angle DEC $ (by reflection or angle calculation).
4. The AA (Angle - Angle) similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Here, $ \angle A=\angle D = 90^\circ $ (right angles) and $ \angle ABC=\angle DEC = 53^\circ $, so AA similarity applies. The first option says "Yes, the AA similarity postulate can be used because a reflection over line $ l $ will establish that $ \angle ABC \cong \angle DEC $" which matches our analysis. The other options are incorrect: the second option refers to side congruence (AA is about angles, not sides), the third option says angles are not congruent (but we proved they are), and the fourth option refers to side congruence (irrelevant for AA).
# Answer:
Yes, the AA similarity postulate can be used because a reflection over line $ l $ will establish that $ \angle ABC \cong \angle DEC $

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