In ∆ABC : AB = 4.8 cm, ∠ A = 90°, AC = 6.8 cm and in ∆XYZ : XY = 4.8 cm, ∠ X = 90° , ZX = 6.8 cm. Are the two triangles congruent by RHS congruence rule?
Question
In ∆ABC : AB = 4.8 cm, ∠ A = 90°, AC = 6.8 cm and in ∆XYZ : XY = 4.8 cm, ∠ X = 90° , ZX = 6.8 cm. Are the two triangles congruent by RHS congruence rule?
Solution
Yes, the two triangles are congruent by the RHS (Right angle-Hypotenuse-Side) congruence rule.
Here's the step-by-step explanation:
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In both triangles, we have a right angle (∠A and ∠X are 90°).
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The hypotenuses (AC and ZX) are equal (6.8 cm).
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One side (AB and XY) of the two triangles are also equal (4.8 cm).
According to the RHS congruence rule, if in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.
So, ∆ABC is congruent to ∆XYZ by RHS congruence rule
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