Question

In the diagram shown below, ∠K=18º and ∠H=18º.

Prove KJ=13.75. Justify your steps in a paragraph proof.

Answer 1

In triangle FGH, ∠G = 112, ∠ H = 18 (GIVEN) , then ∠ F= 180-(112+18) = 50°
In triangle KIJ, ∠ K=18° (GIVEN), ∠J=112° , then ∠ I = 180-(112+18) = 50°

Since Δ FGH & Δ KJI have all their respective angles EQUAL, then these

2 triangles are SIMILAR and all their respective sides are proportional.
If so we can write the following proportions:
GF/JI = GH/JK
8/5 = 22/JK. Cross multiplication → 8.JK = (5).(22) → 8.JK = 110
And JK = 110/8 → JK = 13.75 (JK or KJ are the same)

Answer 2

(See the attached graphic)
Since all 3 angles of each triangle are equal, the triangles are similar.

Since the triangles are similar, all 3 sides must be in the same proportion.

8 / 5 = 22 / KJ

(5 * 22) / 8 = KJ

KJ = 13.75