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Erika is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She begins by assigning coordinates to the vertices of a rectangle as shown.
Erika is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She begins by assigning coordinates to the vertices of a rectangle as shown.Which sentence describes what Erika should do to prove that the diagonals of the rectangle are congruent?
Show that the slope of KM¯¯¯¯¯¯¯ is ba and the slope of JL¯¯¯¯¯ is −ba.
Show that the diagonals intersect at (a2, b2) .
Show that JL=KM=a2+b2−−−−−−√.
Show that JL¯¯¯¯¯ and KM¯¯¯¯¯¯¯ have the same midpoint.
Answer:Option C is the correct choice.Step-by-step explanation:We are given the coordinates of rectangle and we are asked to find the correct option that describes that diagonals JL and KM are congruent.Since we that a rectangle have four right angles.We will use Pythagorean theorem to prove that diagonals JL and KM are congruent.In triangle KLM we can see that KL is b units long and LM is a units long. By Pythagorean theoremIn triangle JML we can see that JM is b units long and LM is a units long. By Pythagorean theoremTherefore, we can see thatand option C is the correct choice....
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