1. Write a two-column proof for the following conjecture. Given: K is the midpoint of . Prove: is an isosceles triangle.

Mathematics

1 answer:

Over [174]3 years ago

7 0

1. Angle LKM and Angle JKM are supplementary 1. LJ is a straight line, since K is a midpoint
2. LK = KJ 2. K is a midpoint
3. Angle L + Angle M + Angle LKM = Angle LKM + Angle MJK 3. A triangle's total degrees is equal to the total degrees of two supplementary angles.
4. Angle JKM = Angle L + Angle M 4. Simple Algebra: Subtract Angle
5. LK = KM 5. MK is intersecting LJ at a midpoint.
6. Triangle LKM is isoceles 6. Two of three sides and angles are equal.

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Answer and Step-by-step explanation: The triangles are plotted and shown in the attachment.

SAS Similarity Theorem is by definition: if two sides in one triangle are proportional to two sides of another triangle and the angles formed by those sides in each triangle is congruent, the triangles are similar.

For the triangles on the grid, we know that ΔJKL and ΔJMN have a congruent angle in J as shown in the image. To prove they are similar, we find the slope of sides KL and MN:

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slope = $\frac{y_{K} - y_{L} }{x_{K} - x_{L} }$