Question

Triangle QRS has been translated to create triangle Q'R'S'. RS= R'S' = 10 units, QS= Q'S' = 5 units, and angles Q and Q' are both 90 degrees. Which theorem below would prove the two triangles are congruent?

 A. SSS
B. SAS
C. ASA
D. HL

Answer 1

Answer: D. HL

Explanation:

Given: Triangle QRS has been translated to create triangle Q'R'S'

such that RS= R'S' = 10 units,

QS= Q'S' = 5 units,

∠Q =∠ Q'= 90°

∴ Both the triangles are right triangles.

Now, the side opposite to ∠Q in Triangle QRS = RS

and the side opposite to ∠Q'in Triangle Q'R'S' = R'S'

Also, the side opposite to the right angle is the hypotenuse of the triangle.

∴ In ΔQRS and ΔQ'R'S'

RS= R'S' = 10 units [Hypotenuse]

QS= Q'S' = 5 units [Leg]

∠Q =∠ Q'= 90° [right angle]

∴ By HL theorem,

ΔQRS ≅ ΔQ'R'S'

• HL theorem tells that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Answer 2

If triangle QRS has been translated to create triangle Q'R'S'. RS= R'S' = 10 units, QS= Q'S' = 5 units, and angles Q and Q' are both 90 degrees. Then the theorem that would prove the two triangles are congruent through the HL theorem. HL stands for Hypotenuse Leg Theorem which states that any two right triangles that has the same or equal hypotenuse and a corresponding equal leg of the 2 triangles, are congruent triangles.