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Question
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
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Solution
In ΔABC and ΔXYZ
AC = XZ
BC = XY
The included angle ∠C = 80° is not equal to ∠X i.e. 70°.
Now, for ΔABC to be congruent to ΔXYZ, AB should be equal to XY and YZ should be equal to BC. Then, ∠A = ∠C and ∠X = ∠Z. So, the measure of ∠B will not be equal to ∠Y.
Therefore, ΔABC cannot be congruent to ΔXYZ.
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