English Medium इयत्ता ९ - CBSE Question Bank Solutions for Mathematics

In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN. 

ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles. 

ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles  

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

Sides opposite to equal angles of a triangle may be unequal 

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

Angles opposite to equal sides of a triangle are equal 

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

The measure of each angle of an equilateral triangle is 60° 

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

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.  

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

The bisectors of two equal angles of a triangle are equal 

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

If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. 

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

The two altitudes corresponding to two equal sides of a triangle need not be equal. 

Fill the blank in the following so that the following statement is true. 

Sides opposite to equal angles of a triangle are ...... 

Fill the blank in the following so that the following statement is true. 

Angle opposite to equal sides of a triangle are ..... 

Fill the blank in the following so that the following statement is true. 

In an equilateral triangle all angles are ..... 

Fill the blank in the following so that the following statement is true. 

In a ΔABC if ∠A = ∠C , then AB = ...... 

Fill the blank in the following so that the following statement is true. 

If altitudes CE and BF of a triangle ABC are equal, then AB = .... 

Fill the blank in the following so that the following statement is true. 

In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.

Fill the blank in the following so that the following statement is true. 

In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……

In a ΔABC, if ∠B = ∠C = 45°, which is the longest side? 

In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle. 

In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC