Question

(a) What additional information is needed to prove the triangles are congruent by ASA Postulate? Explain.

(b) What additional information is needed to prove the triangles are congruent by the HLTheorem? Explain.

Answer 1

Part (a)

ASA = angle side angle

To use ASA, we need two angles and a side between those angles. We already have one pair of angles (DFE and GHI). The other pair of angles must be DEF and GIH to have the side sandwiched between the angles.

Answer: We need to know if angle DEF is congruent to angle GIH

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Part (b)

HL = hypotenuse leg

The sides EF and IH are congruent to one another because of the tickmarks. They are the legs of each right triangle. So that takes care of the "L" of "HL". We need to have the hypotenuses congruent to each other to be able to use HL. This theorem only applies to right triangles.

Answer: We need to know if segment DE is congruent to segment GI