Question

true or false
ABC is an isosceles triangle with AB = AC and AD ⊥ BC. Is ∆ADB ≅ ∆ACD ?

In ∆ABC : AB = 4.8 cm, ∠ A = 90°, AC = 6.8 cm and in ∆XYZ : XY = 4.8 cm, ∠ X = 90° , ZX = 6.8 cm. Are the two triangles congruent by RHS congruence rule? *

Answer 1

Explanation:

ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Fig). To prove that ∠BAD = ∠CAD, a student proceeded as follows: In Δ ABD and Δ ACD, AB = AC (Given) ∠B = ∠C (because AB = AC) And ∠ADB = ∠ADC Therefore, Δ ABD Δ Δ ACD (AAS) So, ∠BAD = ∠CAD (CPCT) What is the defect in the above arguments? [Hint: Recall how ∠B = ∠C is proved when AB = AC]Read more on Sarthaks.com - https://www.sarthaks.com/870590/abc-is-an-isosceles-triangle-with-ab-ac-and-d-is-a-point-on-bc-such-that-ad-bc-fig