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 PM2 = QM . MR
Question 3. In Fig. 6.53, ABD is a triangle right angled at A and AC ⊥ BD. Show that
(i) AB2= BC . BD
(ii) AC2= BC . DC
(iii) AD2= BD . CD
Question 4. ABC is an isosceles triangle right angled at C. Prove that AB2=2AC2
Question 5. ABC is an isosceles triangle with AC = BC. If AB2= 2AC2, prove that ABC is a right triangle.
Question 6. ABC is an equilateral triangle of side 2a. 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.