Question

Show that triangle BCD is isosceles

Answer 1

Step-by-step explanation:

∠BAC = ∠BCA because it is an isosceles triangle

∠ADB = ∠ABD = 72° because it is an isosceles triangle

∠BAD = 180° - 72° - 72° = 36° because the sum of all interior angles in a triangle = 180°

∠BDC = 180° - 72° = 108° because it is supplementary to 72°

∠ABC = 180° - 36° - 36° = 108° because the sum of all interior angles in a triangle = 180°

∠DBC = 108° - 72° = 36°  (∠ABC - ∠ABD)

since ∠DBC = ∠DCB, ΔBCD is isosceles

Answer 2

∠A = 36
∠C =36
∠ADB =72°
∠CBD =36°
∠BDC =108°

Explanation:

AB=AD then ∠ABD & ∠ADB must be equal as they share two lines that are equal so ∠ADB=72°

∠A and ∠C must also be equal (AB=BC)
∠A = 180-72-72=36°
So ∠A & ∠C=36°

∠D=180° (straight line)
So if ∠ADC=72
∠BDC=108° (180-72)

A triangle has 180° so in triangle BDC we have 108° and 36°
So remaining angle (∠CBD) =180-108-36
=36°

This tells us that triangle BDC is isosceles as it has two equal angles ∠CBD & ∠C =36°