ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
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Answer:
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Step-by-step explanation:
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Answered by
1
Step-by-step explanation:
In △ABD and △BCD,
AB=BC ....Sides of a rhombus
AD=CD ....Sides of a rhombus
AC=AC ....Common side
△ABD≅△BCD ...SSS test of congruence
∴∠ABD=∠CBD ....C.P.C.T.
∴∠ADB=∠CDB ....C.P.C.T.
So, Diagonal BD bisects ∠B and ∠D of the rhombus ABCD.
Similarly we can prove,
△ABC≅△ADC
∴∠BAC=∠DAC ....C.P.C.T.
∴∠BCA=∠DCA ....C.P.C.T
So, Diagonal AC bisects ∠A and ∠C of the rhombus ABCD.
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