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29 April, 17:57

Use the information below to find F such that triangle ABC is congruent with triangle DEF. A B equals 36, BC equals 24, D equals 48, M angle B equals 110, I am angle equals 110, EF equals?

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  1. 29 April, 18:00
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    Answer: ∠F = 23° and EF = 24

    Step-by-step explanation:

    Since if two triangles are congruent,

    Then, their corresponding sides and angles must be congruent.

    Since, In Δ ABC and Δ DEF,

    Sides AB, BC and CA are corresponding to sides DE, EF and FD respectively.

    Also, ∠A, ∠B and ∠C are corresponding to ∠D, ∠E and ∠F respectively.

    Therefore, If Δ ABC ≅ Δ DEF

    ⇒ AB ≅ DE, BC ≅ EF and CA ≅ FD

    ∠A ≅ ∠D, ∠B ≅ ∠E and ∠C ≅ ∠ F

    But, It is given that AB = 36 and BC=24

    Therefore, AB = DE = 36 and BC = EF = 24

    Also, m∠B = 110° m∠D = 48°

    ⇒m∠E = 110° and m∠A = 48°

    ⇒m∠F = m∠C = 180 - 158 = 23°
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