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Question
In the given pairs of triangles of the figure, using only RHS congruence criterion, determine which pairs of triangles are congruent. In congruence, write the result in symbolic form:
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Solution
In ∆ABC, by Pythagoras theorem
(AC)2 = (AB)2 + (BC)2
(AC)2 = 62 + 82
(AC)2 = 36 + 64
(AC)2 = 100
(AC)2 = 102
∴ AC = 10 cm
In ∆EDC,
DC = BD – BC = (14 – 8) cm = 6 cm, CE = 10 cm
Now, in ∆ABC and ∆CDE,
∠B = ∠D ...(Each 90°)
AB = CD = 6 cm
AC = CE = 10 cm ...(Hypotenuse)
∴ ∆ABC ≅ ∆CDE ...(RHS criterion)
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