English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm? 

O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC 
(iii) OA + OB + OC >` 1/2`(AB + BC + CA) 

Prove that the perimeter of a triangle is greater than the sum of its altitudes. 

In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC  

Which of the following statements are true (T) and which are false (F)? 

Sum of the three sides of a triangle is less than the sum of its three altitudes. 

Which of the following statements are true (T) and which are false (F)? 

Sum of any two sides of a triangle is greater than twice the median drawn to the third side. 

Which of the following statements are true (T) and which are false (F)? 

Sum of any two sides of a triangle is greater than the third side. 

Which of the following statements are true (T) and which are false (F)? 

Difference of any two sides of a triangle is equal to the third side. 

Which of the following statements are true (T) and which are false (F)? 

If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. 

Which of the following statements are true (T) and which are false (F)?  

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. 

Fill in the blank to make the following statement true. 

In a right triangle the hypotenuse is the .... side. 

Fill in the blank to make the following statement true. 

The sum of three altitudes of a triangle is ..... than its perimeter. 

Fill in the blank to make the following statement true.  

The sum of any two sides of a triangle is .... than the third side. 

Fill in the blank to make the following statement true. 

If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it. 

Fill in the blank to make the following statement true. 

Difference of any two sides of a triangle is........ than the third side. 

Fill in the blank to make the following statement true.  

If two sides of a triangle are unequal, then the larger side has .... angle opposite to it. 

In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.

If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.