Mathematics
ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.
Triangles
13 Likes
Answer
In △APB and △APC,
AB = AC (Given).
∠APB = ∠APC (Both are equal to 90°)
AP = AP (Common)
∴ △APB ≅ △APC by RHS axiom.
We know that corresponding angles of congruent triangles are equal.
∴ ∠B = ∠C.
Hence, proved that ∠B = ∠C.
Answered By
12 Likes
Related Questions
In the adjoining figure, ∠ABC = ∠ACB, D and E are points on the sides AC and AB respectively such that BE = CD. Prove that
(i) △EBC ≅ △DCB
(ii) △OEB ≅ △ODC
(iii) OB = OC.
In the adjoining figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that △ABC ≅ △DEF.
In the adjoining figure, ∠BCD = ∠ADC and ∠BCA = ∠ADB. Show that
(i) △ACD ≅ △BDC
(ii) BC = AD
(iii) ∠A = ∠B
ABCD is a rectangle. X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.