# 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.