The side lengths of triangle RST are 5, 12, and 13. Which set of ordered pairs form a triangle that is congruent to triangle RST?

(-3,-2), (-3,11), (9,-2)

(1,-3), (6,-3), (6,10)

(2,-1) (7,-1), (2,11)

(5,1), (1,13), (12,1)

(2, - 1), (7, - 1), (2, 11) form a triangle congruent to ΔRST

The third answer

Step-by-step explanation:

* The lengths of the sides of triangle RST are 5, 12, 13

∵ 5² + 12² = 25 + 144 = 169

∵ 13² = 169

∴ The sum of the squares of the shortest sides equals

the square of the longest side

∴ Triangle RST is right triangle

* lets find in each answer two sides ⊥ to each other and

then find the lengths of the sides to check which triangle

is congruent to triangle RST

∵ (-3, - 2) and (-3, 11)) have same x-coordinates

∴ the segment joining them is vertical withe length = 11 - - 2 = 13

∵ (-3, - 2) and (9, - 2) have same y-coordinates

∴ the segment joining them is horizontal withe length = 9 - - 3 = 12

∵ The two perpendicular sides have length 12 and 13

∵ In triangle RST the two perpendicular sides are 5 and 12

∴ The first answer not form a Δ congruent to Δ RST

∵ (1, - 3) and (6, - 3)) have same y-coordinates

∴ the segment joining them is horizontal withe length = 6 - 1 = 5

∵ (6, - 3) and (6, 10) have same x-coordinates

∴ the segment joining them is vertical withe length = 10 - - 3 = 13

∵ The two perpendicular sides have length 5 and 13

∵ In triangle RST the two perpendicular sides are 5 and 12

∴ The second answer not form a Δ congruent to Δ RST

∵ (2, - 1) and (7, - 1)) have same y-coordinates

∴ the segment joining them is horizontal withe length = 7 - 2 = 5

∵ (2, - 1) and (2, 11) have same x-coordinates

∴ the segment joining them is vertical withe length = 11 - - 1 = 12

∵ The two perpendicular sides have length 5 and 12

∵ In triangle RST the two perpendicular sides are 5 and 12

∵ The length of the 3rd side = √[ (7 - 2) ² + (-1 - 11) ²] =

√ [5³ + (-12) ²] = √ [25 + 144] = √169 = 13

∵ The length of the hypotenuse of triangle RST = 13

∴ The third answer form a Δ congruent to Δ RST