alternate exterior angles are congruent
When two parallel lines are intersected by a transversal line, alternate exterior angles are formed
When two parallel lines are intersected by a transversal line, alternate exterior angles are formed. Alternate exterior angles are a pair of angles that are on opposite sides of the transversal and are located outside the parallel lines.
The key property of alternate exterior angles is that they are congruent to each other. Congruent angles have the same measure, so if two angles are alternate exterior angles, they will be equal in size.
To better understand this concept, let’s consider the following diagram:
/———————–/
/ /
/ ⇓ /
/_____________/
In the above diagram, the two lines that are parallel to each other are represented by horizontal lines. The slanted line that intersects the parallel lines is the transversal. The pairs of alternate exterior angles are indicated by the symbol “⇓” and the lines that connect them.
According to the alternate exterior angle theorem, the angles on the opposite sides of the transversal, formed by the parallel lines, will have equal measures. Thus, if angle A and angle B are alternate exterior angles, we can say that angle A is congruent to angle B.
This property of congruent alternate exterior angles can be useful when solving various geometric problems involving parallel lines and transversals. It allows us to establish relationships between angles and make calculations based on their congruence.
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