Question

Actually 50 points! Pleas help quickly and only answer if you know the answer!

The following uses a 4-step proof, starting with the given statement. Complete the following proof Given: JK is perpendicular to MN Prove: <1, <2 are complementary.

Answer 1

1. JMN is perpendicularly bisected

2.JMK and JKN are right triangles

3.∠JKM is a right angle

4. ∠1 and ∠2 are complementary

Explanation:

1. Reasoning: Given

2. Reasoning: Definition of a perpendicularly bisected triangle.

3. Reasoning: Definition of a right triangle

4. Reasoning: Triangle Sum Theorem.

Explanation of 4: Because of the Triangle Sum Theorem, which dictates the interior angles of a triangle add up to 180, the other two angles have to add up to 90 or face violating the theorem. Angles that add up to 90 are complementary.

Answer 2

1. JMN is perpendicularly bisected.

2. JMK and JKN are right triangles.

3. ∠JKM is a right angle.

4. ∠1 and ∠2 are complementary.

Explanation:

1. Reasoning: given

2. Reasoning: definition of a perpendicularly bisected triangle.

3. Reasoning: definition of a right triangle.

4. Reasoning: triangle sum theorem.