Proof that Base Angles of an Isosceles Trapezium are Equal

An isosceles trapezium is a quadrilateral with one pair of parallel sides and the other pair of non-parallel sides being of equal length. To prove that the base angles of an isosceles trapezium are equal, we can follow the steps below:

Step 1: Draw an Isosceles Trapezium
- Start by drawing an isosceles trapezium with one pair of parallel sides and the other pair of non-parallel sides being of equal length.

Step 2: Label the Trapezium
- Label the trapezium with the given information, such as side lengths and angles.

Step 3: Identify the Properties of an Isosceles Trapezium
- Recall that in an isosceles trapezium, the non-parallel sides are equal in length, and the base angles are equal.

Step 4: Use the Properties to Prove the Base Angles are Equal
- Since the non-parallel sides are equal in length, the two triangles formed by the diagonal are congruent by Side-Angle-Side (SAS) criteria.
- By congruency, the corresponding angles of the congruent triangles are equal. This includes the base angles of the trapezium.
- Therefore, the base angles of an isosceles trapezium are equal.

By following these steps and understanding the properties of an isosceles trapezium, we can prove that the base angles of the trapezium are indeed equal.