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Theorem 7.5 RHS congruency (Right Angle - Hypotenuse - Side).jpg

Theorem 7.5 - Chapter 7 Class 9 Triangles - Part 2

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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) AB﷮2 ﷯= AC﷮2 ﷯− BC﷮2 ﷯ AB﷮2 ﷯= DF﷮2 ﷯− EF﷮2 ﷯ AB﷮2 ﷯= DE﷮2 ﷯ AB = DE ∴ In ∆ABC and ∆DEF AB = DE BC = EF AC = DF ⇒∆ABC ≅ ∆DEF Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.