Question

Determine whether triangle TJD is congruent to triangle SEK

given
T (-4,-2), J (0,5), D (1,-1), S (-1,3), E (3,10), K (4,4)
and explain the reason.

Choose one answer.
a. No, by AAS
b. Yes, by SAS
c. No, by ASA
d. Yes, by SSS

Answer 1

|TJ| = sqrt((0 - (-4))^2 + (5 - (-2))^2) = sqrt(4^2 + 7^2) = sqrt(65)
|SE| = sqrt((3 - (-1))^2 + (10 - 3)^2) = sqrt(4^2 + 7^2) = sqrt(65)
|JD| = sqrt((1 - 0)^2 + (-1 - 5)^2) = sqrt(1^2 + (-6)^2) = sqrt(37)
|EK| = sqrt((4 - 3)^2 + (4 - 10)^2) = sqrt(1^2 + (-6)^2) = sqrt(37)
|DT| = sqrt((-4 - 1)^2 + (-2 - (-1))^2) = sqrt((-5)^2 + (-1)^2) = sqrt(26)
|KS| = sqrt((-1 - 4)^2 + (3 - 4)^2) = sqrt((-5)^2 + (-1)^2) = sqrt(26)^2

Since the corresponding sides of the two triangles are equal. the two triangles are congruent by SSS.