NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.2

Question 4

Step 1: Note the given lengths from the figure.

• \(PB = 5\,\text{cm}\)
• \(PC = 6\,\text{cm}\)
• \(PD = 10\,\text{cm}\)
• \(PE = 12\,\text{cm}\)

Step 2: Write the ratios of the sides of the two triangles.

For \(\triangle PBC\) and \(\triangle PDE\):

\[ \dfrac{PB}{PD} = \dfrac{5}{10} = \dfrac{1}{2}, \quad \dfrac{PC}{PE} = \dfrac{6}{12} = \dfrac{1}{2} \]

Step 3: Compare the included angle.

At point \(P\), the angle \(\angle BPC\) and the angle \(\angle DPE\) are equal because they are vertically opposite angles.

Step 4: Apply the SAS (Side–Angle–Side) similarity rule.

Since:

• Two pairs of sides are in the same ratio (\(\dfrac{1}{2}\)), and
• The included angle between those sides is equal,

Therefore, \(\triangle PBC \sim \triangle PDE\).