In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be c

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Question: In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?

Options:

Correct Answer: ABCD is a parallelogram.

Solution:

If both pairs of opposite sides are equal, then ABCD is a parallelogram.

In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?

In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?

Step 1: Identify the quadrilateral ABCD and label its sides: AB, BC, CD, and AD.
Step 2: Note the given information: AB is equal to CD (AB = CD) and AD is equal to BC (AD = BC).
Step 3: Understand the property of a parallelogram: A quadrilateral is a parallelogram if both pairs of opposite sides are equal.
Step 4: Since AB = CD and AD = BC, both pairs of opposite sides are equal.
Step 5: Conclude that quadrilateral ABCD is a parallelogram based on the property of equal opposite sides.

Properties of Quadrilaterals – Understanding the properties of quadrilaterals, specifically that if both pairs of opposite sides are equal, the quadrilateral is a parallelogram.
Congruence and Equality – Recognizing that equal lengths of opposite sides imply certain properties about the shape and classification of the quadrilateral.