# Theorem 7.5

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Theorem 7.5 (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 triangle are congruent . Given :- Two right triangles ∆ABC and ∆DEF where ∠B = 90° & ∠E = 90°, hypotenuse is equal i.e. AC = DF & one side is equal i.e. BC = EF To Prove :- ∆ABC ≅ ∆DEF Proof:- From (1) AB2 = AC2 − BC2 AB2 = DF2 − EF2 AB2 = DE2 AB = DE ∴ In ∆ABC and ∆DEF AB = DE BC = EF AC = DF ⇒∆ABC ≅ ∆DEF Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.