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 = 2KLSTATEMENT:1.) K is the midpoint of MJ. L is the midpoint of NJ.2.) MK ≅ KJ and NL ≅ LJ3.) MK = KJ AND NL = LJ4.) MJ = MK + KJ and NJ = NL + LJ5.) MJ = 2KJ and NJ = 2LJ6.) MJ/KJ = NJ/LJ = 27.) 8.) Triangle JMN ~ Triangle JKL9.) MN/KL = MJ/KJ10.) MN/KL = 211.) MN = 2KLREASON:1.) Given2.) ???3.) ???4.) ???5.) Substitution Property of Equality6.) Division Property of Equality7.) ???8.) ???9.) ???10.) ???11.) ???
Question
Answer:
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.
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