Question

prove that opposite angles of a parallelogram are equal​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Question:

prove that opposite angles of a parallelogram are equal​ ?

Given:

ABCD is parallelogram in which

• AC is the diagonal

• AB = CD

• AD = BC

To Prove:

• ∠A = ∠C

• ∠B = ∠D

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

Solution:

ABCD is a parallelogram

AC is the diagonal

AB = CD

AD = BC

To Prove:

∠A = ∠C

∠B = ∠D

Proof:

In ΔABC and ΔADC

• AC = AC ( Common Side )

• AB = CD ( Opposite angles of a parallelogram are equal )

• AD = BC ( Opposite angles of a parallelogram are equal )

By SAS Congruency criterion ΔABC ≅ ΔADC

• ∠A = ∠C ( By CPCT )

• ∠B = ∠D ( By CPCT )

Answer:

• ∠A = ∠C ( By CPCT )

• ∠B = ∠D ( By CPCT )

Prove that in a parallelogram, opposite sides are equal.​

Refer to https://brainly.in/question/14945970