Question

Triangle ABC is an isoceles triangle in which AB=CD.AD bisects angle PAC and CD is parallel to AB.show that :-i) angleDAC=angleBCA amd show that quadrilateral ABCD is a Parallelogram

Answer 1

by theorem 8.8 if in a quadrilateral on pair of opposite sides is equal and parallel then the quadrilateral is a parallelogram..In quadrilateral ABCD ,AB=CD and AB parallel to CD . therefore ABCD is a parallelogram...since ABCD is a parallelogram therefore AC is it's diagonal ..and alternate angles are equal ..
Therefore angle DAC =angle BCA..