Perfection is not attainable, but if we chase perfection we can catch excellence. – **Vince Lombardi**

# Lecture - 10 Chapter 6 Triangles

**NCERT Exercise 6.5**

**Question 1.** Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

**Question 2.** PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM^{2} = QM . MR

**Question 3.** In Fig. 6.53, ABD is a triangle right angled at A and AC ⊥ BD. Show that

(i) AB^{2}= BC . BD

(ii) AC^{2}= BC . DC

(iii) AD^{2}= BD . CD

**Question 4.** ABC is an isosceles triangle right angled at C. Prove that AB^{2}=2AC^{2}

**Question 5.** ABC is an isosceles triangle with AC = BC. If AB^{2}= 2AC^{2}, prove that ABC is a right triangle.

**Question 6.** ABC is an equilateral triangle of side 2*a*. Find each of its altitudes.

**Question 7.** Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.