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MAR DIONYSIUS SENOIR SEC SCHOOL RISHI VALLEY, MALLAPALLY, Kerala, India-689534 Paper : IX Mathematics Lines, Angles and Triangles Q.1 Find out whether the following statements are true or not? Correct the statement if it is not true. (i) Through two distinct points infinite number of lines can be drawn. (ii)If AB=EF and CD = EF then AB=CD. (iii)A terminated line cannot be produced any further. (iv)If m is a line and P is a point not on the line then there can be ifinite number of lines passing through P which are parallel to m (Marks : 2 ) Q.2 If B lies between two points A and C, AC = 9 cm and AB is half of BC. Find AB and BC. Q.3 What are the properties of parallel and intersecting lines? Q.4 (Marks : 2 ) Prove that two distinct lines in a plane cannot have more than one point in common. Q.5 What are collinear points and concurrent lines? Explain with diagrams. Q.6 Given three distinct points in a plane, how many lines can be drawn through them? Q.7 Prove that if two lines intersect, the vertically opposite angles are equal. Q.8 (Marks : 2 ) AOC and BOC form a linear pair. Determine the value of x. (Marks : 2 ) (Marks : 2 ) (Marks : 2 ) (Marks : 2 ) (Marks : 2 ) Q.9 Write the complement of each of the following angles. (i) 20o (ii) 34o (Marks : 2 ) Q.10 What is the measure of an angle which is equal to one-third of its supplement? Q.11 If AX is a bisector of Q.12 Two angles are adjacent and form an angle of 135o. The larger is 15o more than three times the smaller. Find the angles. (Marks : 2 ) Q.13 (i) Write the complement of each of the following: (a) 30o (b) 70o (ii) Write the supplement of each of the following: (a) 132o (b) 124o (Marks : 2 ) Q.14 If the difference between any two supplementary angles is equal to one right angle, then find the angles. (Marks : 2 ) Q.15 In a triangle ABC, the angles ABC and ACB are given to be equal. If the side BC is produced both ways, show that the exterior angles so formed are equal. Q.16 300 persons are sleeping in a hall. Prove that the area of the floor occupied by all the persons is less than the area of the floor of the hall. (Marks : 3 ) Q.17 There are two vessels A and B. ''A'' contains 3 litre of milk and ''B'' contains 3 litre of water. If two smaller BAC such that BAX = 37o, find the measure of (Marks : 2 ) BAC. (Marks : 2 ) containers of equal volumes C and D are filled from A and B respectively such that 2.5 find the amount of water left in container B. (Marks : 3 ) (Marks : 2 ) milk is left in ''A'', Q.18 Prove that two lines which are both parallel to the same line are parallel to each other. Q.19 If R lies between P and Q and PR is twice RQ and PQ = 15 m, find PR and RQ. Q.20 Prove that the bisectors of a pair of vertically opposite angles are in the same straight line. Q.21 In the given figure, ray OP bisects 3) Q.22 Find the measure of the supplement of the following angles. (i) 158o (ii) 134o (iii) 72o (Marks : 3 ) Q.23 Two complementary angles are such that two times the measure of one is equal to three times the measure of BOC and ray OQ bisects (Marks : 3 ) (Marks : 3 ) AOC. Show that (Marks : 3 ) POQ = 90o. (Marks : the other. Determine the measure of the smaller angle. Q.24 (Marks : 3 ) Lines AB and CD are parallel and P is any point between the two lines as shown in the figure. Prove that + CDP = DPB ABP (Marks : 3 ) Q.25 Property: If a transversal intersects two lines, making a pair of alternate interior angles equal, then the two lines are parallel. Prove it. (Marks : 3 ) Q.26 Prove that if a transversal intersects two parallel lines, then each pair of consecutive interior angles (the interior angles on the same side of the transversal) are supplementary. (Marks : 3 ) Q.27 Prove that if a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. (Marks : 3 ) Q.28 If a transversal cuts two parallel lines, prove that the bisectors of the interior angles form a rectangle. :5) (Marks