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Andrew is writing a coordinate proof to show that the triangle formed by connecting the midpoints of the sides of an isosceles triangle is itself an isosceles triangle. He starts by assigning coordinates as given.
Enter the answers in the boxes to complete the coordinate proof.
P is the midpoint of DE¯¯¯¯¯. Therefore, the coordinates of P are (
, b).
Q is the midpoint of DF¯¯¯¯¯. Therefore, the coordinates of Q are (3a,
).
R is the midpoint of EF¯¯¯¯¯. Therefore, the coordinates of R are (
,
).
The length of PR¯¯¯¯¯ is a2+b2−−−−−−√ . The length of QR¯¯¯¯¯ is a2+b2−−−−−−√.
Comparing the expressions for the lengths of PR¯¯¯¯¯ and QR¯¯¯¯¯ shows that the lengths are equal. Therefore, △PQR is isosceles.
