Corresponding Angles

Definition: If two lines are intersected by a transversal (third line):
Corresponding angles are two angles in the same position (matching corners), of different intersections. When the two lines crossed by a transversal are parallel, the corresponding angles are equal.

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Example: Identify pairs of corresponding angles:

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Solution:

Use the definition to identify a pair of corresponding angles.

Step 1: We know corresponding angles are located in the same position (or matching corners) of different intersections.Intersections are formed where the transversal crosses the pair of lines. In this figure, there are two intersections: an intersection is formed where Line t crosses Line l, and another is formed where Line t crosses Line m.

Angles ∠1, ∠2, ∠3 and ∠4 are formed in the top intersection, while angles ∠5, ∠6, ∠7 and ∠8 make up the bottom intersection.
Comparing these intersections will allow us to identify our corresponding angles.

Step 2: In the top intersection, ∠1 is in the top left position, ∠2 is in the top right, ∠3 is in the bottom left, and ∠4 is in the bottom right position. In the bottom intersection, ∠5 is in the top left position, ∠6 is in the top right, ∠7 is in the bottom left and ∠8 is in the bottom right position.

The definition tell us that corresponding angles will be in the same position of different intersections.From this information we can determine the following pairs of corresponding angles:

∠1 and ∠5 are corresponding angles because they are both in the top left position of their intersections.
∠2 and ∠6 are corresponding angles because they are both in the top right position of their intersections.
∠3 and ∠7 are corresponding angles because they are both in the bottom left position of their intersections.
∠4 and ∠8 are corresponding angles because they are both in the bottom right position of their intersections.

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