In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE? The triangles are not similar because only one pair of corresponding angles is congruent. The triangles are similar because all right triangles can be mapped to each other using a series of transformations. The triangles are not similar because they share a common segment and vertex. The triangles are similar because all pairs of corresponding angles are congruent.
Answers
Step-by-step explanation:
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Given : In the diagram m∠A = 55° and m∠E = 35°. and few statements
To Find : The statements which explains the relationship between Δ ACB and Δ DCE
Solution:
Ref attached picture
∠ACB = ∠DCE = 90°
in ΔABC
∠A + ∠B + ∠ACB = 180°
=> 55° + ∠B + 90° = 180°
=> ∠B = 35°
in ΔDEC
∠D + ∠E + ∠DCE = 180°
=> ∠D + 35° + 90° = 180°
=> ∠D = 55°
in ΔACB & ΔDCE
∠A = ∠D = 55°
∠ACB = ∠DCE = 90°
∠B = ∠E = 35°
=> ΔACB ≈ ΔDCE
=> The triangles are similar because all pairs of corresponding angles are congruent.
The triangles are similar because all pairs of corresponding angles are congruent.
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