Question

What other information do you need to prove GHK ≅ KLG by SAS?

The image is a quadrilateral GHKL and a diagonal GK is drawn such that it forms two triangles GHK and KLG. Sides GL and KH are marked as congruent.

A. ∠KHG ≅ ∠GLK
B. ∠HGK ≅ ∠LKG
C. ∠GHK ≅ ∠KLG
D. ∠HKG ≅ ∠LGK

Answer 1

Question:

What other information do you need to prove ∆ GHK ≅ ∆ KLG by SAS?

Answer:

HKG ≅ LGK

Answer 2

Answer: D. ∠HKG ≅ ∠LGK

Explanation:

Given: Quadrilateral GHKL where diagonal GK is drawn such that it forms two triangles GHK and KLG.

Side GL ≅ Side KH

Now, GK is common in both triangles GHK and KLG.

and GK ≅GK

SAS congruence rule: If any two sides and the angle included between the sides of one triangle are congruent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent.

So ∠HKG must be congruent to ∠LGK ( angles between the congruent sides).

Hence, the correct option is D. ∠HKG ≅ ∠LGK