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NCERT STD 10 Maths- Triangles | Part-16| Exercise-6.5|Problems(1,2 &3) solutions
This class handles solutions to the following problems

6.5.1 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)Â Â 7cm,24cm,25cm

(ii)Â Â 3cm,8cm,6cm

(iii)Â Â 50cm,80cm,100cm

(iv)Â Â 13cm,12cm,5cm

6.5.2 PQR is a triangle right angled at P and M is a point on QR such that PM âŠ¥ QR. Show that PM2Â = QM â€¢ MR.

6.5.3. In the given figure, ABD is a triangle right angled at A and AC i. BD. Show that

(i) AB2Â = BC.BD

(ii) AC2Â = BC.DC

(iii) AD2Â = BD.CD

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NCERT CBSE Class 10 Maths Solutions- Part-17| Exercise-6.5|Problems(4,5,6 &7)
This video handles solutions to the following problems in Textbook

6.5.4. ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.

6.5.5. ABC is an isosceles triangle with AC = BC. If AB2 = 2 AC2, prove that ABC is a right triangle.

6.5.6. ABC is an equilateral triangle of side 2a. Find each of its altitudes.

6.5.7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
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PART 18- Class 10 Mathematics| NCERT / CBSE solutions: Exercise-6.5|Problems(8,9 & 10)
In this class teacher explains the solutions of the following problems

8. In Fig. 6.54, O is a point in the interior of a triangle ABC, OD âŠ¥ BC, OE âŠ¥ AC and OF âŠ¥ AB.

Show that

(i) OA2 + OB2 + OC2 â€“ OD2 â€“ OE2 â€“ OF2 = AF2 + BD2 + CE2,

(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2.Â
9. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.Â
10. 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?
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NCERT Class 10 Maths Video Lessons
Triangles | Part-19| Class 10|Exercise-6.5|Problems(11,12 & 13 )
In this class teacher will help you to find out the solutions of the following problems

Â

6.5.11. 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 1/ 2 hours?

Â
6.5.12. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

Â 6.5.13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2.
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NCERT Class 10 Maths Video Lessons
Triangles | Part-20| Class 10|Exercise-6.5 solutions|Problems(14,16, 16 & 17)
In this class teacher will help you to find out the solutions to the following problems

14. The perpendicular from A on side BC of a Î” ABC intersects BC at D such that DB = 3 CD (see Fig. 6.55). Prove that 2 AB2 = 2 AC2 + BC2.
15. [b]Â [/b]In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3BC. Prove that 9AD2Â = 7AB2

16. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

17. Tick the correct answer and justify :

In Î” ABC, AB = 63 cm, AC = 12 cm and BC = 6 cm. The angle B is :

(A) 120Â° (B) 60Â° © 90Â° (D) 45Â°

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