Two right-angled triangular blocks, ABC and DEF, have ∠B = ∠E = 90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?
Yes, by RHS
Step 1 – Identify the given matching parts:
(i) Right angle at B = Right angle at E, (ii) Hypotenuse AC = Hypotenuse DF, (iii) Side AB = Side DE.
Step 2 – Recall the RHS rule:
Two right-angled triangles are congruent if the Right angle, the Hypotenuse, and one corresponding Side are equal — exactly the three pieces given here.
Step 3 – Conclusion:
\(\triangle ABC \cong \triangle DEF \quad \text{(by RHS)}\)
Hence the answer is Yes, by RHS — option 3.
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Important Questions from Triangles, Congruence and Similarity
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What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
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