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Nadya [2.5K]
3 years ago
14

Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE We are given AB ∥ DE. Because the lines are parallel and segment CB crosses bo

th lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA. We can state ∠C ≅ ∠C using the reflexive property. Therefore, △ACB ~ △DCE by the AA similarity theorem. SSS similarity theorem. AAS similarity theorem. ASA similarity theorem.
Mathematics
2 answers:
Arturiano [62]3 years ago
6 0

Answer: AA similarity theorem.

Step-by-step explanation:

Given : AB ∥ DE

Prove: ΔACB ≈ ΔDCE

We are given AB ∥ DE. Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA.

Also ∠C ≅ ∠C using the reflexive property.

Therefore by AA similarity theorem , ΔACB ≈ ΔDCE

  • AA similarity theorem says that if in two triangles the two pairs of corresponding angles are congruent then the triangles are similar .
noname [10]3 years ago
6 0

Answer:

AA

Step-by-step explanation:

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