Question

Is it possible to show that angle G is congruent to angle K

Answer 1

Angle g and k are congruent because angle HG is congruent to JK as you can tell with the two red marks

Answer 2

Yes , it is possible that ∠ G is congruent to ∠ K .

Explanation:

As

In ΔIKH and ΔIGJ .

(1) IJ = IH (Given)

(2)∠KIH = ∠GIJ (Common angle of both triangles.)

(3) IK=IG

(As given IJ = IH , JK = HG

IJ + JK = IH + HG

IK = IG )

Thus by using SAS congurence property .

ΔIKH ≅ ΔIGJ

Thus

∠G = ∠K

(By using the corresponding sides of the congurent triangles .)

Thus ∠G = ∠K