Class 9 Triangles Important Questions

Important Questions

Triangles Important Questions

1. Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A. Show that:
   1. ΔAPB ≅ ΔAQB
   2. BP = BQ or B is equidistant from the arms
      of ∠A.
      
2. In ΔABC, ∠A – ∠B = 33° and ∠ B – ∠ C = 18°. Find the measure of each angle of the triangle.
3. In the given Figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
   
4. ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST
5. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B. Show that:
   1. AMC ≅ ΔBMD
   2. ∠DBC is a right angle.
   3. ΔDBC ≅ ΔACB
   4. CM = 1/2 AB
      
6. The angles of the triangle are in the ratio 2:3:7. Find the measure of each angle of the triangle. 
7. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal.
   
8. Two adjacent angles on a straight line are in a ratio 5:4. Find the measure of each one of these angles.
9. ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.
10. ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST.
11. In the given figure, AB = BC and ∠ABO = ∠CBO, then prove that ∠DAB = ∠ECB.
    
12. In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that 
    1. ΔPTR ≌ ΔRMP     
    2. RT || PM and
    3. RT = PM
       
13. ABC is a triangle in which AB=AC. If D be a point on BC produced, prove that AD>AC.
14. If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.