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The Given Figure Shows a Triangle Abc in Which Ad is Perpendicular to Side Bc and Bd = Cd. Prove That: (I) ∆ Abd ≅ ∆ Acd (Ii) Ab = Ac (Iii) ∠B = ∠C - Mathematics

Sum

The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ ABD ≅ ∆ ACD
(ii) AB = AC
(iii) ∠B = ∠C

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Solution

(i) In the given figure Δ ABC

AD ⊥ BC, BD = CD

In Δ ABD and Δ ACD

AD = AD ............(common)

∠ADB = ∠ADC ...............(each 90°)

BD = CD ...........(Given)

∴ Δ ABD ≅ Δ CAD .........(By SAS Rule)

(ii) Side AB = AC .........(c.p.c.t.)

(iii) ∠B = ∠C

Reason, since Δ ADB ≅ Δ ADC

∴ ∠B = ∠C

Hence proved.

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
  Is there an error in this question or solution?
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 15
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