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

Advertisement Remove all ads

#### 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?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads