Question

Prove the following theorems.

1. If two lines are perpendicular, then they meet to form right angles.
2. If two angles are complementary to the same angle (or to congruent angles), then these angles are congruent.
3. If two angles are supplementary to the same angle (or to congruent angles), then these angles are congruent.

Answer 1

Answer:

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Answer 2

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1.The linear pair perpendicular theorem states that when two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular. A linear pair of angles is such that the sum of angles is 180 degrees. As the angles measure 90 degrees, the lines are proved to be perpendicular to each other..

2.If two angles are each complementary to a third angle, then they're congruent to each other. (Note that this theorem involves three total angles.) Complements of congruent angles are congruent. If two angles are complementary to two other congruent angles, then they're congruent.....

3.If two angles are supplementary to the same angle (or to two congruent angles) then the two angles are congruent. (Proof): Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other.....

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