Chapter 10 Congruent Triangles RD Sharma Solutions Exercise 10.6 Class 9 Maths
Chapter Name  RD Sharma Chapter 10 Congruent Triangles Exercise 10.6 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 10.6 Solutions
1. In Î”ABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
Solution
Sum of angles in a triangle 180°
2. In a Î”ABC, if ∠B = ∠C = 45° , which is the longest side ?
Solution
Given that in Î”ABC,
∠B = ∠C = 45°
We have to find longest side
We know that,
Sum of angles in a triangle = 180°
3. In Î”ABC, side AB is produced to D so that BD = BC. If ∠B = 60°, ∠A = 70° , prove that :
(ii) AD > AC
First join C and D
2 + 7 > 3
and 3 + 7 > 2
Here, 2 + 3 ⊁ 7 So, the triangle does not exit.
(iii) OA + OB + OC > 1/2(AB + BC + CA)
We have to prove
(iii) OA + OB + OC > 1/2(AB + BC + CA)
AB + BC > AC
In Î”OAC
In Î”OAB
Now, extend (or) produce BO to meet AC in D.
(ii) CD + DA + AB > BC
(ii) CD + DA + AB > BC
8. Which of the following statement are true (T) and which are false (F)?
(i) Sum of the three sides of a triangle is less than the sum of its three altitudes.
(ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
(iii) Sum of any two sides of a triangle is greater than the third side.
(iv) Difference of any two sides of a triangle is equal to the third side.
(v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
(vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Solution
(i) False (F)
Reason: Sum of these sides of a triangle is greater than sum of its three altitudes
(ii) True (F)
(iii) True (T)
(iv) False (F)
Reason: The difference of any two sides of a triangle is less than third side.
(v) True (T)
Reason: The side opposite to greater angle is longer and smaller angle is shorter in a triangle
(vi) True (T)
Reason: The perpendicular distance is the shortest distance from a point to a line not containing it.
9. Fill in the blanks to make the following statements true.
(i) In a right triangle the hypotenuse is the ...... side.
(ii) The sum of three altitudes of a triangle is ..... than its perimeter.
(iii) The sum of any two sides of a triangle is .... than the third side.
(iv) If two angles of a triangle are unequal, then the smaller angle has the side opposite to it.
(v) Difference of any two sides of a triangle is than the third side.
(vi) If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
Solution
(i) In a right triangle the hypotenuse is the largest side.
Reason : Since a triangle can have only one right angle, other two angles must be less than 90°.
⇒ The right angle is the largest angle.
⇒ Hypotenuse is the largest side.
(ii) The sum of three altitudes of a triangle is less than its perimeter.
(iii) The sum of any two sides of a triangle is greater than the third side.
(iv) If two angles of a triangle are unequal, then the smaller angle has the smaller side opposite to it.
(v) Difference of any two sides of a triangle is less than the third side.
(vi) If two sides of a triangle are unequal, then the larger side has greater angle opposite to it.