CBSE TEST PAPER CLASS - IX Mathematics (Congruent triangle)

1. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

(A) an isosceles triangle (B) an obtuse triangle (C) an equilateral triangle (D) a right triangle

2. An exterior angle of a triangle is 105° and its two interior opposite angles are  equal. Each of these equal angles is

(A) 37+ 1/2°  (B)52+ 1/2° (C) 72+ 1/2° (D) 75°

3. The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is

(A) an acute angled triangle (B) an obtuse angled triangle  (C) a right triangle (D) an isosceles triangle

4 . If one of the angles of a triangle is 130°, then the angle between the bisectors of  the other two angles can be      

(A) 50° (B) 65° (C) 145° (D) 155°

5. The sum of two angles of a triangle is equal to its third angle. Find the third angles.

(a) 90⁰  (b) 45⁰ (c) 60⁰ (d) 70⁰                                                    

Section B

1. If two lines intersect, prove that the vertically opposite angles are equal.

2. Bisectors of interior ∠B and exterior ∠ACD of a D ABC intersect at the point T. Prove that < BTC =1/2 
<∠ BAC.

3. A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so 
formed are parallel.

4. Prove that through a given point, we can draw only one perpendicular to a given line. [Hint: Use proof by 
contradiction].

5. Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

6.  In DABC , ∠Q > ∠R, PA is the bisector of ∠QPR and PM ^QR. Prove that <∠APM = 1/2(∠< Q – 
∠<R).

7. A triangle ABC is right angled at A. L is a point on BC such that AL ^  BC. Prove that ∠ < BAL = ∠ < 
ACB


8. Q is a point on the side SR of a Δ PSR such that PQ = PR. Prove that PS > PQ. 


9. S is any point on side QR of a Δ PQR. Show that: PQ + QR + RP > 2 PS.


10. D is any point on side AC of a Δ ABC with AB = AC. Show that CD < BD. 


11. l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment  CD, having its end points on l and m, respectively. 


12. Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is 
produced to a point M. Prove that ∠MOC =∠ABC.


13. Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. 
Show that external angle adjacent to ∠ABC is equal to ∠BOC. 

14. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. {Produce QS to intersect PR 
at T}

15. Prove that in a right triangle, hypotenuse is the longest (or largest) side

CBSE Exam  Congruence of Triangle Solved Questions

Q. 1. Prove that Sum of Two Sides of a triangle is greater than twice the length of median drawn to third side.

Given: Δ ABC in which AD is a median.

To prove: AB + AC > 2AD.

Construction: Produce AD to E, such that AD = DE. Join EC

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