Show that triangle BCD is isosceles

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

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