Understanding Congruent Angles | Definition, Examples, and Properties

congruent angles

Congruent angles are angles that have the same measure or size

Congruent angles are angles that have the same measure or size. In other words, if two angles have the same degree measurement, they are said to be congruent. The symbol used to denote congruent angles is an equal sign with a wavy line on top (∼), which is read as “congruent to”. For example, if angle A is congruent to angle B, we write it as ∠A ≅ ∠B.

Congruent angles can be found in many different situations. Some common cases include:

1. Vertical angles: Vertical angles are a pair of non-adjacent angles formed by two intersecting lines. The two pairs of vertical angles are always congruent to each other. For example, if angle 1 and angle 3 are vertical angles, then ∠1 ≅ ∠3.

2. Corresponding angles: Corresponding angles are formed when a transversal intersects two parallel lines. These angles are located in the same position relative to the transversal, one on each of the parallel lines. Corresponding angles are congruent to each other. If angle A and angle B are corresponding angles, then ∠A ≅ ∠B.

3. Alternate interior angles: Alternate interior angles are formed when a transversal intersects two parallel lines, and they are located on opposite sides of the transversal. Like corresponding angles, alternate interior angles are congruent. If angle A and angle B are alternate interior angles, then ∠A ≅ ∠B.

4. Alternate exterior angles: Alternate exterior angles are also formed when a transversal intersects two parallel lines, but they are located on opposite sides of the transversal and outside the parallel lines. Like the previous cases, alternate exterior angles are congruent. If angle A and angle B are alternate exterior angles, then ∠A ≅ ∠B.

It is important to note that congruent angles have the same measure, but their orientation or position may be different. Congruent angles can be rotated or flipped, but they will still have the same degree measurement.

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