Mathematics, 16.12.2020 09:30, daltonrebekah3440

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-column proof of the theorem is shown, but the proof is incomplete.

A triangle with vertices A is at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE with point D on side AB and point E is on side BC

Statement Reason
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula
Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 By the distance formula
Segment DE is half the length of segment AC By substitution
Slope of segment DE is −2 and slope of segment AC is −2
Segment DE is parallel to segment AC Slopes of parallel lines are equal
Which of the following completes the proof? (6 points)

By definition of congruence
Addition property of equality
By construction
By the slope formula

Answers: 2

Show answers

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 23:30, Cklug2520

Apyramid fits exactly inside a cube. the cube and the pyramid share the same square base, and they are both exactly the same height. the volume of the cube is 66 cubic inches. what is the volume of the pyramid? explain your answer. answer asap

Answers: 1

continue

Mathematics, 22.06.2019 01:30, bethanybowers4986

Jahdzia wears her winter coat when the temperature is colder than -4 degrees celsius. write an inequality that is true only for temperatures (t) at which jahdzia wears her winter coat.

Answers: 3

continue

Mathematics, 22.06.2019 03:00, ddarby

Barrett is comparing the membership fees for two museums. the art museum charges a one-time fee of $8.25 plus $2.25 per month. the science museum charges a one-time fee of $10.75 plus $3.50 per month. how much does barrett save by joining the art museum instead of the science museum?

Answers: 3

continue

Mathematics, 22.06.2019 03:40, calibaby1220

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. complete parts (a) through (c) below. a. if 1 adult female is randomly selected, find the probability that her pulse rate is between 65 beats per minute and 79 beats per minute. the probability is? b. if 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 65 beats per minute and 79 beats per minute. the probability is? c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Answers: 3

continue

Do you know the correct answer?

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side...