# Important Questions for Chapter 6 - Triangles

The set of important questions carries step-by-step explanation and solution to the given questions. You just need to go through them and prepare well for your exams. No more hassles of finding the answer yourself too!

**Important questions based on NCERT syllabus for Chapter 6 - Triangles:**

*Question 1*: In the given figure, If PQ∥RS, prove that ΔPOQ∼ΔSOR.

*Solution*:

PQ∥RS [Given]

⇒∠P=∠S [Pair of alternate angles]

and ∠Q=∠R [Pair of alternate angles]

Also, ∠POQ=∠SOR [Vertically opposite angles]

∴ΔPOQ∼ΔSOR [AAA similarity criterion]

*Question 2*: If ΔABC∼ΔDEF such that area of ΔABC is 9 cm^2 and the area of ΔDEF is 16 cm2 and BC = 2.1 cm. Find the length of EF.

*Solution*:

We have ,

ΔABC∼ΔDEF

⇒ area (ΔABC)/area (ΔDEF)=BC^2/EF^2

⇒ 9/16 = (2.1)^2/EF^2

⇒ 3/4 = 2.1/EF

⇒ EF = 4 × 2.1/3 cm = 2.8 cm

*Question 3*: A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

*Solution*:

Let AB be the ladder and CA be the wall with the window at A.

Given, BC = 2.5 m and CA = 6 m

Since wall and window are perpendicular to each, applying Pythagoras Theorem, we have:

AB^2 =BC^2 + CA^2

AB^2 = (2.5)^2 + (6)^2

AB^2 = 6.25 + 36

AB^2 = 42.25

⇒ AB = 6.5

Thus, length of the ladder is 6.5 m.