Determine wether triangle deef is cogruent to triangle pqr given the coordinates of the verticles. D(-6,1),E(-1,-4),P(0,5),Q(7,6),R(5,0)
The length of DE equals the length of PR, which means that congruence is not impossible.
However, the coordinates of F is missing, so it is not possible to determine if DEF is congruent to PQR.
Well, by a simple vector calculation in the plane, you can easily find the last verticle. However, I interpret the question just as MathMate did.
To determine whether triangle DEEF is congruent to triangle PQR, we need to compare their corresponding sides and angles. Here's how you can do it step by step:
1. Calculate the lengths of the sides of each triangle:
- For triangle DEEF:
a. Calculate the length of EF:
EF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-1 - (-6))^2 + (-4 - 1)^2)
b. Calculate the length of DE:
DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-6 - (-1))^2 + (1 - (-4))^2)
c. Calculate the length of DF:
DF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((-1 - (-6))^2 + (-4 - 1)^2)
- For triangle PQR:
a. Calculate the length of QR:
QR = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((7 - 0)^2 + (6 - 5)^2)
b. Calculate the length of PQ:
PQ = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((0 - 0)^2 + (5 - 6)^2)
c. Calculate the length of PR:
PR = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((5 - 0)^2 + (0 - 5)^2)
2. Compare the side lengths:
Check if the lengths of the corresponding sides of the two triangles are equal:
- DE = QR
- EF = PQ
- DF = PR
If all the corresponding sides are equal, then the triangles are congruent under the side-side-side (SSS) congruence criterion.
3. Compare the angles:
- Calculate the measures of the angles in each triangle:
- For triangle DEEF: measure of angle DEE, measure of angle DEF, & measure of angle DFE
- For triangle PQR: measure of angle PQR, measure of angle PRQ, & measure of angle QPR
Check if the measures of the corresponding angles in the two triangles are equal.
If all the corresponding angles are equal, then the triangles are congruent under the angle-angle-angle (AAA) congruence criterion.
By performing these calculations and comparisons, you will be able to determine if triangles DEEF and PQR are congruent.