IX Lines and Angles and Triangles: Questions From CBSE Examination Papers Chapter:

CBSE SAMPLE PAPER   2012-2013                                  Class IX- Triangles

Q.1 If DABC @ DDEF and if AB=3.5 = DE and BC = EF = 5.5, then necessary condition is

(a) ÐA = ÐD (b) ÐB = ÐE (c)ÐC = ÐF (d) CA = FD

Q.2 In DPQR,ÐR = ÐP and QR = 3cm and PR = 4.5cm. Then the length of PQ is

(a) 3cm (b) 5cm (c) 2 cm (d) 2.5cm.

Q.3 ABC is an isosceles triangle with AB = AC. Draw AP ^ BC . Then

(a) ÐB = ÐC (b) ÐB + ÐC = 90⁰ (c) AP=BP (d) BP≠PC.

Q.4 In the given figure OP = OQ and OS= OR. Then which is false?

(a) DPOS @ DQOR (B) RQ=FS (c) DPOS @ DQOR (d) None of these

Q.5 In DABC, ÐA = 100° and AB = AC, then ÐB = 

(a) 40° (b) 60° (c) 30° (d) None of these

Q 6 . Which of the following is not a criterion for congruence of triangles?
(A) SAS (B) ASA (C) SSA (D) SSS
Q 7. . If AB = QR, BC = PR and CA = PQ, then
(A) Δ ABC ≅ Δ PQR (B) Δ CBA ≅ Δ PRQ  (C) Δ BAC ≅ Δ RPQ (D) Δ PQR ≅ Δ BCA
Q. 8  In Δ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to
(A) 40° (B) 50° (C) 80° (D) 130°

Section B . 2 Mark Each

Q.9 In the given figure, AC = AE, AB =AD and ÐBAD = ÐEAC , show that BC = DE.

Q.10 Prove that each angle of an equilateral triangle is 60°.

Q 11. In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side AB of Δ ABC so that the two triangles are congruent? Give reason for your answer.
Q 12 . In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of Δ PQR should be equal to side BC of Δ ABC so that the two triangles are congruent? Give reason for your answer.
Q. 13 . AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.
Section C . 3 Mark Each
Q.14 D is a point on side BC of DABC such that AD = AC. Show that AB> AD.

Q 15. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR.

Q 16. If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

Q 17. P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that BPQ is an isosceles triangle.

Section D . 4 Mark Each

Q.18 Prove that any two sides of a triangle are together greater than twice the median  drawn to the third side.

Q.19 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

(i) DAMC @ DBMD (ii) ÐDBC is a right angle (iii)DDBC @ DACB (iv) CM = 1/2 AB

Q. 20. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. { Produce QS to intersect PR at T}
CBSE SAMPLE PAPER- Lines Angles class IX 
Section A MCQ . 1 Mark Each
Q.1 An angle is 16° more than its complement. Then its measure is
(a) 42° (b) 48° (c) 53° (d) 68°
Q.2 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.
Q.3 the necessary conditions for the lines l and m to be parallel, when these lines are intersected by a transversal line .n. is that
(a) Interior angles on the same side are equal. 
(b) Corresponding angles are equal 
(c ) Vertically opposite angles are equal. 
(d) Corresponding angles are not equal.
Q.4 One angle forming a linear pair is twice the other. The larger is
(a) 120° (b) 60° (c) 160° (d) None of these
Q.5 co interior angles are also called ____ angles
(a) allied (b) alternate (c) complementary (d) None of these
Section B  2 Mark Each

Q.6 In figure , AE bisects ÐBAD and ÐB = ÐC . Prove that AF || BC .
Q.7 In the figure  lines XY and MN intersect at O,If 0 ÐPOY = 90 and a : b = 2 : 3, find c.

Section C . 3 Mark Each 

Q.8 In the figure  the side QR of triangle PQR is produced to a point S. If the bisectors of ÐPQR and ÐPRS meet at point T, then prove that <QTR= 1/2 <QPR.

Section       D 4 Mark Each

Q.9 In the figure, m and n are two plane mirrors parallel to each other. Show that the incident ray CA is parallel to the reflected ray BD.

 Q.10 In figure BD bisects ÐEBC , CD bisects ÐFCB . Prove < BDC=  90 – 1/2<A