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}
Construction: Produce AD to E, such that AD = DE. Join EC
(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.
9th Geometry: Triangle Test Paper Download File
Triangles Solved Questions Paper Download File
CBSE IX Congruence of Triangle Solved Questions Download File
Triangles Solved Questions Paper Download File
CBSE IX Congruence of Triangle Solved Questions Download File
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