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Read the proof.

Given: AEEC; BDDC

Prove: △AEC ~ △BDC



Statement Reason
1. AEEC;BDDC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ? 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
What is the missing statement in step 4?

∠ACE ≅ ∠ACE
∠EAB ≅ ∠DBC
∠EAC ≅ ∠EAC
∠CBD ≅ ∠DBC

Read the proof Given AEEC BDDC Prove AEC BDC Statement Reason 1 AEECBDDC 1 given 2 AEC is a rt BDC is a rt 2 definition of perpendicular 3 AEC BDC 3 all right a class=

Respuesta :

Okay so It is given that ∠ABR and ∠ACR are right angles, AB ≅ BC and BC ≅ AC Since they contain right angles, △ABR and △ACR are right triangles. The right triangles share hypotenuse AR, and reflexive property justifies that AR ≅ AR. Since AB ≅ BC and BC ≅ AC, the transitive property justifies AB ≅ AC. Now, the hypotenuse and leg of right △ABR is congruent to the hypotenuse and the leg of right △ACR, so △ABR ≅ △ACR by the HL congruence postulate. Therefore, ∠BAR ≅ ∠CAR by CPCTC, and bisects ∠BAC by the definition of bisector.
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Answer:

the answer is A. <ACE = <ACE


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