Question

Abc is an isosceles triangle with ba=bc d lies on ac.Abd is an isosceles triangle with ab=ad angle abd=72 show that triangle bcd is isosceles.You must give a reason for each working out.

Answer 1

A property of an isosceles triangle, which is the base angles of the are

equal, can be used to show that ΔBCD us an isosceles triangle.

• ΔBCD is an isosceles triangle :- definition of an isosceles triangle

Reasons:

Let ∠DAB = ∠A, ∠DCB = ∠C, ∠ABC = ∠B

The steps to show that ΔABD is an isosceles triangle are as follows;

∠ABD = 72° = ∠ADB :- Base angles of the isosceles triangle ΔABD

∠A + ∠ABD + ∠ADB = 180° (angle summation property)

∠A = 180° - (∠ABD + ∠ADB) = 180° - (72° + 72°) = 36°

∠A = ∠C :- Base angles of the isosceles triangle ΔBDC

∠ADB = ∠C + ∠DBC :- Exterior angle of a triangle theorem

72° = ∠C + ∠DBC

∠BDC = 72° + ∠A

∠DBC + ∠BDC + ∠C = 180° (angle summation property)

∠DBC = 180° - (∠BDC + ∠C) = 180° - (72° + 36° + 36°) = 36°

∠DBC = 36° = ∠C

In ΔBCD, ∠DBC = ∠C

• ΔBCD is an isosceles triangle :- definition of an isosceles triangle

The base angles of an isosceles triangle are equal.

https://brainly.com/question/1675130