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,––3,,–2)
(1,–,–,10)
(2,–1)(7,–,11)
(5,,,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

24: 56

step-by-step explanation:

24 can be divided into 3 and 56 can be divided into 7, where as all the other ratios can't.

each side has a different length.  

step-by-step explanation: