Question 167637
Given: Triangle MLP is isosceles, N is the midpoint of MP
Prove: LN is perpendicular to MP
2 column chart
so far i have done
Triangle MLP is isoscele - Given
ML is congruent to PL- Def. of isosceles triangle
N is the midpoint of MP- Given
MN is congruent to PN- Def. of midpoint
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Angle LNM is congruent to Angle LNP- Linear Pair angles are congruent
THIS SHOULD BE:
angle LMN = angle LPN - if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent also.
i believe you were referring to the base angles of the isosceles triangle, and not the angles formed at the midpoint of MP.
base angles of the triangle are LMN and LPN.
angles formed at the midpoint are LNM and LNP.
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Triangle LNM is congruent to Triangle LPN- SAS
THIS IS OK.
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now that you have that triangle LMN congruent to triangle LPN, you can prove that angle LNM congruent to angle LNP.
reason:
corresponding angles of congruent triangles are congruent.
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then you can show that angle LNM is supplementary to angle LNP.
reason:
if the exterior sides of two adjacent angles form a straight line, then the angles are supplementary.
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then you can show that angle LNM + angle LNP = 180 degrees.
reason:
if 2 adjacent angles are supplementary, then the sum of their angles is 180 degrees.
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then you can show that angle LNM and angle LNP are each equal 90 degrees.
reason:
angle LNM + angle LNP = 180 degrees.
this is the same as 2 * angle LNM = 180 degrees (substitution of equals)
this means angle LNM = 180 / 2 = 90 degrees (algebra)
this means that angle LNP = 90 degrees (equal to angle LNM).
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then you can show that LN is perpendicular to MP
reason:
2 lines intersecting at 90 degrees angle are perpendicular to each other.
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