Math, asked by aman609, 1 year ago

the opposite angle of parallelogram equal probe that

Answers

Answered by sethrollins13
25

✯✯ QUESTION ✯✯

Prove that opposite angles of parallelogram are equal..

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✰✰ ANSWER ✰✰

⠀⠀⠀⠀⠀⠀(Refer to the attachment)

Given : -

  • AB = CD
  • BC = AD

To Prove : -

  • \angle{A}=\angle{C}
  • \angle{B}=\angle{D}

Proof : -

In Δ ABC and Δ ADC : -

\longmapsto\tt{AB=CD} (Given)

\longmapsto\tt{BC=AD} (Given)

\longmapsto\tt{AC=AC} (Common)

So , By SAS Rule Δ ABC Δ ADC...

Now ,

\longmapsto\tt{\angle{D}=\angle{B}} (By CPCT Rule)

Similarly ,

\longmapsto\tt{\angle{A}=\angle{C}} (By CPCT Rule)

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SSS Rule : -

If three sides of one triangle are equal to the three sides of another triangle then the two angles are congruent.

CPCT means Corresponding Parts of Congruent Triangle.

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