5.4k views
2 votes
Read the proof.

Given: aeec; bddc
Prove: △aec ~ △bdc
1.aeec;bddc | Given
2.∠aec is a rt. ∠; ∠bdc is a rt. ∠ | Definition of perpendicular
3.∠aec ≅ ∠bdc | All right angles are congruent
4.? | Reflexive property
5.△aec ~ △bdc | AA similarity theorem
What is the missing statement in step 4?
a) ∠ace ≅ ∠ace
b) ∠eab ≅ ∠dbc
c) ∠eac ≅ ∠eac
d) ∠cbd ≅ ∠dbc

1 Answer

3 votes

Final answer:

The missing statement in step 4 using the Reflexive Property for proving that triangles AEC and BDC are similar is 'c) ∠eac ≅ ∠eac'. option c is the correct answer.

Step-by-step explanation:

The student is given that the lines ae and ec are perpendicular, as well as bd and dc. They have to prove that triangles △aec and △bdc are similar.

The definition of perpendicular lines tells us that ∠aec and ∠bdc are right angles, making them congruent based on the fact that all right angles are congruent. For step 4 of the proof, we need to use the Reflexive Property to identify a side or angle that is equal to itself within the two triangles.

Since ∠eac is an angle in both △aec and △bdc, the correct option in the final answer is 'c) ∠eac ≅ ∠eac'. With two pairs of congruent angles, the two triangles are similar by the AA similarity theorem.

User Matt Haughton
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.