Congruence of Triangles By RHS Criteria
Congruence of Triangles by RHS Criteria
Theorem: Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other triangle.
Given: Two right triangles ABC and DEF in which
To Prove:
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Construction: Produce FE to G so that GE = BC. Join GD. Proof: In BC = GE [By construction] and, AB = DE [Given] So, by SAS criterion of congruence, we have
and, AC = DF [Given] Using (i) and (2) we have DF = DG
From (ii) and (iii), we get Thus, in Adding equations (1) and (2), we have
Now, in AB = DE [ Given ] and, AC = DF [ Given ] So, by SAS criterion of congruence, we have Hence, |
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Illustration: If is an isosceles triangle such that AB = AC and AD is an altitude from A on BC. Prove that (i)
(ii) AD bisects BC (iii) AD bisects
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Solution: In right triangles ADB and ADC, we have Hyp. AB = Hyp. AC [Given] AD = AD [common side] So, by RHS criterion of congruence, we have
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Name five theorems that prove triangles are congruent. | |||
| Right Option : A | |||
| View Explanation | |||
In | |||
| Right Option : B | |||
| View Explanation | |||
In the figure shown above, if AP = AC, AB = AM , then
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| Right Option : D | |||
| View Explanation | |||
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