1. 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. 2. In DABC , ∠Q > ∠R, PA is the bisector of ∠QPR and PM ^QR. Prove that <∠APM = 1/2(∠< Q – ∠<R). 3. D ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle. 4. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. 6. Example 5. If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles. 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. Related posts: PDF Download CLICK HERE CBSE Sample Questions Papers Maths Ch: Triangle IX Mathematics Congruence of Triangle CBSE Examination Question 2012-13 CBSE Test sample paper- IX Mathematics (Congruent triangle) CBSE TEST PAPER CLASS - IX Mathematics (Congruent triangle)
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omer
1/4/2015 12:53:34 pm
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