CLASS 9TH CBSE MATHS CHAPTER  TRIANGLE CBSE TEST PAPER1
1. PQ = PR of < QPR and S and T are point on PR and PQ such that ∠PQS = ∠PRT . Prove that Δ PQS ≅ Δ PRT. 2. Two lines AB and CD intersect each other at the point O such that BC  DA and BC = DA. Show that O is the midpoint of both the linesegments AB and CD( join BC and AD) 3. In triangle P Q R , PQ > PR and QS and RS are the bisectors of ∠Q and ∠R, respectively.Show that SQ > SR 4. ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE. 5. D and E are points on side BC of a Δ ABC such that BD = CE and AD = AE. Show that Δ ABD ≅ Δ ACE. 6. CDE is an equilateral triangle formed on a side CD of a square ABCD (join AE and BE). Show that Δ ADE ≅ Δ BCE. 7. BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that Δ ABC ≅ Δ DEF .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 midpoint of a line segment AB. Show that M is also the midpoint 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. AD is the bisector of ∠BAC. of DABC . Prove that AB > BD. 15. ABC is a right triangle and right angled at B such that ∠BCA = 2 ∠BAC. AD perpendicular to BC. Show that hypotenuse AC = 2 BC. 16. Prove that if in two triangles two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent. 17. If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles. 18. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. { Produce QS to intersect PR at T} CBSE TEST PAPER2 1 marks questions 1. Which of the following is not a criterion for congruence of triangles? (A) SAS (B) ASA (C) SSA (D) SSS 2 . 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 3 . In Δ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to (A) 40° (B) 50° (C) 80° (D) 130° 2 marks questions 1. 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. 2 . 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. 3 . 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. 3 marks questions 1. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. 2. If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles. 3. 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. 4 marks questions 1. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side 2. Show that in a quadrilateral AB + BC + CD + DA < 2 (BD + AC) 3. In a right triangle, prove that the linesegment joining the midpoint of the hypotenuse to the opposite vertex is half the hypotenuse.
21 Comments
kavita tewani
26/8/2011 08:58:14 pm
Prove that sum of any two sides of a triangle
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27/8/2012 03:18:08 am
Given: ΔABC in which AD is a median.
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rajeev
2/9/2013 06:29:50 pm
p is a mid point on the bisector of angle abc .if the line through p, parallel to ba meets bc at q, provethat bpq is an isosceles triangle.
srishtijaiswal
9/9/2013 09:36:50 pm
correct diya misra .....this is the correct method to do this question
y
22/9/2014 03:59:17 am
make other triangle
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alia
1/11/2015 10:35:11 am
How to solve
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srishti jaiswal
9/9/2013 09:42:03 pm
Quesif O is a point within triangleABC,show that:AB+BC+CA>OA+OB+OC
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srishti jaiswal
10/9/2013 04:34:26 pm
tell the answer to my question plz.......exams are approaching....
Reply
30/8/2014 09:03:04 pm
Pizazz can u ans this question that: show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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jsunil
31/8/2014 11:07:39 pm
Q. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest
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Alekhya
22/2/2015 08:33:19 am
Thanks
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Alan
16/8/2016 07:02:06 am
1st question answer
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Shaaista Hasan
11/9/2016 08:41:56 pm
I think this can b proved only d triangles are right angled triangles....
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Shaaista hasan
11/9/2016 08:14:34 pm
ABCD is a quadrilateral. 'P' is a point in the interior of the quadrilateral. AP and DP are the angle bisectors of <A and <D.
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Shaaistahasan
11/9/2016 08:49:12 pm
Plz fast i have an exam
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