Monday 12 September 2011

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

9th Geometry: Triangle Test Paper                                     Download File
Triangles Solved Questions Paper                                      Download File 
CBSE IX Congruence of Triangle Solved Questions            Download File

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