• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5.

  • Triangles Class 10 Ex 6.1
  • Triangles Class 10 Ex 6.2
  • Triangles Class 10 Ex 6.3
  • Triangles Class 10 Ex 6.4
  • Triangles Class 10 Ex 6.5
  • Triangles Class 10 Ex 6.6
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 6
Chapter Name Triangles
Exercise Ex 6.5
Number of Questions Solved 17
Category NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5

Ex 6.5 Class 10 Maths 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
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 66

Ex 6.5 Class 10 Maths 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 X MR.
Solution:
In a right triangle, perpendicular drawn from right angle to hypotenuse divides the triangle into two similar triangles
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 67

Ex 6.5 Class 10 Maths Question 3.
In the given figure, ABD is a triangle right angled at A and AC i. BD. Show that
(i) AB2 = BC.BD
(ii) AC2 = BC.DC
(iii) AD2 = BD.CD

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 68
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 69
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 70

Ex 6.5 Class 10 Maths Question 4.
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 71

Ex 6.5 Class 10 Maths Question 5.
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, Prove that ABC is a right triangle.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 72

Ex 6.5 Class 10 Maths Question 6.
ABC is an equilateral triangle of side la. Find each of its altitudes.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 73
As all the altitudes of an equilateral triangle are equal hence, each of the altitudes of ∆ABC is of length \(\sqrt { 3 } a\).

Ex 6.5 Class 10 Maths 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.
Solution:
The figure given below shows a rhombus ABCD in which AB = BC = CD = DA. The diagonals AC and BD bisect each other at O.
In ∆AOB, ∠AOB = 90°
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 74

Ex 6.5 Class 10 Maths Question 8.
In the given figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
(i) OA2 + OB2 + OC2 – OD2 – OE2 – OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 75
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 76
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 77

Ex 6.5 Class 10 Maths Question 9.
A ladder 10 m long reaches a window 8 m above the ground. ind the distance of the foot of the ladder from base of the wall.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 78

Ex 6.5 Class 10 Maths Question 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?
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 79

Ex 6.5 Class 10 Maths Question 11.
An airplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another airplane 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\(\frac { 1 }{ 2 }\) hours?
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 80

Ex 6.5 Class 10 Maths Question 12.
Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 81
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 82

Ex 6.5 Class 10 Maths Question 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.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 83

Ex 6.5 Class 10 Maths Question 14.
The perpendicular from A on side BC of a ∆ABC intersects BC at D such that DB = 3CD (see the figure). Prove that 2AB2 = 2AC2 + BC2.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 84
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 85

Ex 6.5 Class 10 Maths Question 15.
In an equilateral triangle ABC, D is a point on side BC, such that BD = \(\frac { 1 }{ 3 }\)BC. Prove that 9AD2 = 7AB2.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 86
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 87

Ex 6.5 Class 10 Maths Question 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.
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 88

Ex 6.5 Class 10 Maths Question 17.
Tick the correct answer and justify : In ∆ABC, AB = 6\(\sqrt { 3 } \)cm, AC = 12 cm and BC = 6 cm. The angle B is:
(a) 120°
(b) 60°
(c) 90°
(d) 45

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 89

 

We hope the NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • Development Class 10 Important Questions Social Science Economics Chapter 1
  • Agriculture Class 10 Important Questions Social Science Geography Chapter 4
  • Biomolecules Class 11 Notes Biology Chapter 9
  • NCERT Exemplar Class 10 Maths Solutions Chapter 13 Statistics and Probability
  • Important Questions for Class 12 Computer Science (Python) – Review of Python
  • NCERT Solutions for Class 7 Hindi Vasant Chapter 14 खानपान की बदलती तस्वीर
  • Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration
  • Antonyms and Synonyms Exercises for Class 8 CBSE With Answers – English Grammar
  • NCERT Class 10 Science Lab Manual Cleaning Capacity of Soap in Hard and Soft Water
  • NCERT Solutions for Class 11 Hindi Core – अपठित बोध- अपठित काव्यांश
  • CBSE Revision Notes for Class 10 English First Flight Chapter 2 Nelson Mandela: Long Walk to Freedom
  • ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4
  • Power Sharing Class 10 Important Questions Social Science Political Science Chapter 1
  • Important Questions for CBSE Class 12 Chemistry – The d- and f- Block Elements
  • CBSE Class 12 Business Studies Case Studies – Consumer Protection

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions