Question

ABC is an isosceles triangle with AB = AC and AD is one of its altitudes.

(i) State the three pairs of equal parts in ∆ADB and ∆ADC.
(ii) Is ∆ADB ≅ ∆ADC? Why or why not?
(iii) Is ∠B = ∠C? Why or why not?
(iv) Is BD = CD? Why or why not?

Answer 1

(i) In ∆ADB and ∆ADC,
∠BDA = ∠CDA.................(each 90°)
Side AB = Side AC..........(Given)
Side AD = Side AD.........(Common Side)

(ii) ∆ADB ≅ ∆ADC.......[From (i)]( RHS Congruence Criterion)

(iii) ∠B = ∠C........(Corresponding Angle Congruence test)

(iv) BD = CD........(Corresponding Side Congruence test)