- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Prove that, in a parallelogram

1)opposite sides are equal

2) opposite angles are equal

3) Each diagonal will divide the parallelogram into two congruent triangles

**Given :**

We have to prove that , in a parallelogram,

1)opposite sides are equal

2) opposite angles are equal

3) Each diagonal will divide the parallelogram into two congruent triangles

**Solution :**

Take a parallelogram ABCD and join

Two of its non-adjacent vertices, say A and C.

In the parallelogram ABCD,

BC || AD and AB || DC.

AC is the transversal between the parallel lines BC and AD, and it is also a transversal between the parallel lines AB and DC.

Let the angles formed by these parallel lines and transversal be angles 1, 2, 3 and 4.

Consider ∆ ABC and ∆ CDA,

**∠ 1 = ∠ 3 (since alternate angles are equal)**

**∠ 2 = ∠ 4 (since alternate angles are equal)**

AC = CA (common side)

So, by the ASA rule ∆ ABC ≅ ∆ CDA.

Therefore, **diagonal AC divides**

**parallelogram ABCD into two congruent triangles ABC and CDA**.

In congruent triangles ABC and CDA,

BC = DA (corresponding sides of congruent triangles)

Similarly, BA = DC.

BC and DA; BA and DC are opposite sides in the parallelogram ABCD.

**Therefore, in a parallelogram, opposite sides are equal.**