Question

24) If ABCD is a rhombus, show that each
diagonal bisects the vertex angle through
which it passes.​

Answer 1

AB≅CD [opposite side of parallelogram are congruent.]

BC≅AD[opposite side of parallelogram are congruent.]

AC≅AC [common side]

ΔABC≅ΔADC [SSS]

∠1≅∠4 [cpct]

∠3≅∠2 [cpct]

and,

AB≅BC[sides of a rhombus]

ΔABC is isosceles

∠1≅∠3, ∠1≅∠2, ∠3≅∠4

AC bisects ∠BCD.

hope it will help you.

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