Question

prove that opposite angles are equal in parallelogram is equal​

Answer 1

Answer:

What are the Properties of a Parallelogram?

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In this mini-lesson, we will explore the world of parallelograms and their properties. We will learn about the important theorems related to parallelograms and understand their proofs. So what are we waiting for. Let’s begin!

We all know that a parallelogram is a convex polygon with 4 edges and 4 vertices. The opposite sides are equal and parallel; the opposite angles are also equal.

Let’s play with the simulation given below to better understand a parallelogram and its properties. Try to move the vertices A, B, and D and observe how the figure changes. Observe that at any time, the opposite sides are parallel and equal. Also, the opposite angles are equal. Let’s play along.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Here, ABCD is a parallelogram with AC as its diagonal.

We know, in parallelogram opposites sides are parallel.

So, AB∥DC and AD∥BC

Since, AB∥DC and AC is the transversal

⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]

Similarly, AD∥BC and AC is the transversal.

⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]

Adding ( 1 ) and ( 2 ),

⇒ ∠BAC+∠DAC=∠DCA+∠BCA

⇒ ∠BAD=∠DCB

Similarly, we can prove, ∠ADC=∠ABC

∴ We have proved that, opposite angles of a parallelogram are equal.

solution