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