CBSE Class 10 maths Triangles Ex 6.5 | Problems on Pythagoras Theorem

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Pythagoras Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Converse of Pythagoras Theorem

In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

In this video, we learn how to apply Pythagoras Rule to solve Problems on right-triangles.Use parallel lines concept and triangle similarity theorems to prove problems on solving similar triangles.Many Word problems are solved using Pythagoras Theorem.

Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for class 10 Subject: Maths

This Video is also refers as CBSE class 10 mathts NCERT Solutions Chapter 6 Triangles.

00:03 Q1. 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.

00:34 (i) 7 cm, 24 cm, 25 cm

01:15 Use Pythagoras Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

02:13 Q4. ABC is an isosceles triangle right angled at C. Prove that AB^2 = 2AC^2.

02:28 Pythagoras Theorem Application

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

03:59 Q5. ABC is an isosceles triangle with AC = BC. If AB^2 = 2 AC^2, prove that ABC is a right triangle.

05:32 Use Converse of Pythagoras Theorem

In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

06:00 Q6. ABC is an equilateral triangle of side 2a . Find each of its altitudes.

07:51 AAA similarity criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

09:15 Pythagoras Theorem Application

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

10:10 Result proved Altitude of equilateral triangle formula proof

Altitude of equilateral triangle IS SQRT(3)*(SIDE)/2.

13:12 Word problems Pythagoras Theorem

Q10. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

14:47 Pythagoras Theorem Application

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

16:04 Pythagoras Theorem Word problems

Q11. An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 and 1/2 hours?

19:38 Pythagoras Law

21:30 Worked out Word problems on Pythagoras Theorem.

23:50 Pythagoras Rule

24:58 Q13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE^2 + BD^2 = AB^2 +DE^2.

26:20 Pythagoras Theorem

29:07 Q14. The perpendicular from A on side BC of a? ABC intersects BC at D such that DB = 3 CD(see Fig. 6.55). Prove that 2AB2 =2 AC2 + BC2.

30:54 Pythagoras Theorem

32:35 Deductions to simplify the results

33:27 Q15. In an equilateral triangle ABC, D is a point on side BC such that BD = 13 BC. Prove that 9 AD2 = 7 AB2.

33:44 Consider two triangles & apply Pythagoras Theorem

36:18 AA similarity criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

36:33 conditions for two triangles to be similar

Two triangles are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion)

42:02 Q16. In an equilateral triangle, prove that three times the square of one side is equal to fourtimes the square of one of its altitudes.

43:34 AA similarity rule

44:52 Pythagoras Theorem

46:02 Q17. Tick the correct answer and justify : In ? ABC, AB = 6sqrt3 cm, AC = 12 cm and BC = 6 cm.

The angle B is : (A) 120° (B) 60° (C) 90° (D) 45°

46:45 Converse of Pythagoras Theorem

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CBSE solutions for class 10 maths Chapter 6 Triangles Exercise 6.

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