Question

Provide the missing reasons for the proof of part of the triangle midsegment theorem. Given: K is the midpoint of . L is the midpoint of . Prove: Answer: Statement Reason 1. K is the midpoint of . L is the midpoint of . 1. 2. and 2. 3. and 3. 4. and 4. 5. and 5. Substitution Property of Equality 6. 6. Division Property of Equality 7. 7. 8. ∆JMN≅∆JKL 8. 9. 9. 10. 10. 11. 11.  

Answer 1

Answer:

1. K is the midpoint of MJ - 1. Given

2. L is the midpoint of NJ - 2. Given

3. Angle MJK = Angle LJN - 3. Identity

4. Line segment LK is parallel to MN - 4. Triangle midsegment theorem

5. Angle JKL = Angle JMN, and Angle JLK = Angle JNMN - 5.Transversal

6. Triangle JKL is similar to Triangle JMN - 6. AAA similarity theorem

7. JM = 2JK - 7. Statement 1

8. MN=2KL - 9. Statement 7 and 6

Step-by-step explanation:

Answer 2

To prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

K is the midpoint of MJ.

L is the midpoint of NJ.

It is required to prove: MN = 2KL

From the diagram and table given in the picture:

1. K is MJ's midway. L is where NJ splits in half. ~ Given

2. MK, KJ, and NL, LJ: Midpoint Definition

3. Segment Congruence Postulate: MK=KJ and NL=LJ

4. Segment Addition Postulate: MJ = MK + KJ and NJ = NL + LJ

5. Substitution Property of Equality: MJ = 2KJ, NJ = 2LJ

6. The Division Property of Equality: MJ/KJ = NJ/LJ = 2

7. The Reflexive Property of J

8. The SAS Similarity Theorem, JMN, and JKL

9. Corresponding parts of identical triangles have a proportional relationship (MN/KL = MJ/KJ).

10. Substitution: MN/KL = 2

11. The Multiplication Property of Equality: MN = 2KL

Thus, to prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

Learn more about the triangle here:

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