SarkariPYQ

SSC CHSL 2024 PYQ — Question 66

SSC CHSL - 09 July 2024 - Shift 4 • Quantitative Aptitude • Q66

Back to paper

In the diagram, if AB‾∥CE‾\overline{AB} \parallel \overline{CE}, AG = GD = DH = HB, then which of the following is correct?

I) ΔACG ≅ ΔBEH II) ΔCDE ≅ ΔDEB III) ΔHFB ≅ ΔAFG

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. I and II.

Given that, AB‾∥CE‾\overline{AB} \parallel \overline{CE}

Also, AG = GD = DH = HB

According to the given diagram, 

CG = EH   (Perpendicular distance between two parallel lines)

(I) In triangle ACG and triangle BEH

AG = BH

∠AGC = ∠BHE = 90° 

CG = EH

So, ΔACG ≅ ΔBEH by SAS congruency.

(II) In triangle CDE and triangle DEB,

DE = DE   (common side)

∠CDE = ∠DEB    (corresponding angles)

Let AG = GD = DH = HB = 1

In triangle CDE, CE = GD + DH 

⇒ 1 + 1 = 2

In triangle DEB, DB = DH + HB

⇒ 1 + 1 = 2

⇒ CE = DB

So, ΔCDE ≅ ΔDEB by SAS congruency.

(III) No clear relation is given in triangle HFB and triangle AFG.

Hence only I and II are correct.