Based only on the facts in the diagram, which triangle criterion can you use to prove that ΔABC and ΔABD are congruent?
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Given : ΔABC and ΔABD
To Find : which triangle criterion can you use to prove that ΔABC and ΔABD are congruent?
Solution:
∠ABC = 90° ( Right angle given)
∠ABC + ∠ABD = 180° Linear pair
=> 90° + ∠ABD = 180°
=> ∠ABD = 90°
∠ABC = ∠ABD
in ΔABC and ΔABD
AB = AB Common
∠ABC = ∠ABD = 90°
BC = BD given
ΔABC ≅ ΔABD ( SAS criteria)
SAS triangle criterion can be used to prove that ΔABC and ΔABD are congruent
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