Question

the opposite angle of parallelogram equal probe that

Answer 1

✯✯ 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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