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Provide the missing reasons for the proof of part of the triangle midsegment theorem.

Given: K is the midpoint of MJ. L is the midpoint of NJ.

Prove: MN = 2KL

STATEMENT:
1.) K is the midpoint of MJ. L is the midpoint of NJ.

2.) MK ≅ KJ and NL ≅ LJ

3.) MK = KJ AND NL = LJ

4.) MJ = MK + KJ and NJ = NL + LJ

5.) MJ = 2KJ and NJ = 2LJ

6.) MJ/KJ = NJ/LJ = 2

7.)
8.) Triangle JMN ~ Triangle JKL

9.) MN/KL = MJ/KJ

10.) MN/KL = 2

11.) MN = 2KL

REASON:

1.) Given
2.) ???
3.) ???
4.) ???
5.) Substitution Property of Equality
6.) Division Property of Equality
7.) ???
8.) ???
9.) ???
10.) ???
11.) ???

Provide the missing reasons for the proof of part of the triangle midsegment theorem Given K is the midpoint of MJ L is the midpoint of NJ Prove MN 2KL STATEMEN class=

Respuesta :

2) By definition of the midpoint point. If a point is in the middle of a segment, then the two resulting segment are equal. 
3) Obvious, the point K is on the line MJ.
6) From statement 5 and the property of fractions. 
8) SAS statement of congruent triangles (notice the two triangles share on common angle which is between the two proportional sides)
9) The two corresponding  sides are congruent. 
10) The constant of proportionality is 2. 
11) From statement 10. 
wolfnight2122

Answer:

  1. Given
  2. Definition of Midpoint
  3. Segment Congruence Postulate
  4. Segment Addition Postulate
  5. Substitution Property of Equality
  6. Division Property of Equality
  7. Reflexive Property
  8. SAS Similarity Theorem
  9. Corresponding Parts of Similar Triangles Are Proportional
  10. Substitution
  11. Multiplication Property of Equality

Let me know if these answers are correct.

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