CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Triangles)

 

Important Mathematics Questions of  Class X Chapter {Triangles} for CBSE Examination 2023

1.   If in two triangles, corresponding angles are equal, then the two triangles are……………

2.   ∆ABC is right angled at B. BD is perpendicular upon AC. If AD=a, CD=b, then AB²=

3.   The areas of two similar triangles are 32cm² and 48cm².If the square of a side of the first ∆ is 24cm²,then the square of the corresponding side of 2^nd triangle will be

4.   ABC is a triangle with DE|| BC. If AD=2cm, BD=4cm then find the value DE:BC

5.   In ∆ABC,DE ||BC, if AD=4x-3,DB=3x-1,AE=8x-7and BC=5x-3,then find the values of x

6.   The perimeters of two similar triangles are 40cm and 50 cm respectively, find the ratio of the area of the first triangle to the area of the 2^nd triangle:

7.   A man goes 150m due east and then 200m due north. How far is he from the starting point?

8.   A ladder reaches a window which is 12m above the ground on one side of the street. Keeping its foot at  the same point, the ladder is turned to the other side of the street to reach a window 9m high. If the length   of the ladder is 15m, find the width of the street.

9.   BO and CO are respectively the bisectors of ÐB and ÐC of ∆ABC.AO produced meets BC at P, then find AB/AC 

10. In triangle ABC, the bisector of ÐB intersects the side AC at D.A line parallel to side AC intersects line segments AB,DB and CB at points P,R,Q respectively. Then, Find AB XCQ

11.  If ∆ ABC is an equilateral triangle such that AD^BC, then AD²=………..

12.   If ∆ABC and ∆DEF are similar triangles such that ÐA=47⁰,andÐE=83⁰ ,then find ÐC

13. Two isosceles triangles have equal angles and their areas are in the ratio 16:25,then find the ratio of their corresponding heights

14. Two poles of heights 6m and 11m stand vertically upright on a plane ground.If the distance between their feet is 12m, then find the distance between their tops.

15. The lengths of the diagonals of a rhombus are 16cm and 12cm.Then, find the length of the side of the rhombus .

16. In triangle BD^AC and CE^AB then prove that

(a)∆AEC~∆ADB

(b)CA/AB=CE/DB

17. What is the value of K in given figure if DE||BC.

18. A pole of length 10m casts a shadow 2m long on the ground. At the same time a tower casts a shadow of length 60m on the ground then find the height of the tower.

19.   Find the length of altitude of an equilateral triangle of side 2cm.                                         

20. In a trapezium ABCD,O is the point of intersection of AC and BD,AB||CD and AB=2CD.If the area o  ∆AOB=84cm² then find area of ∆COD. 

21. D and E are points on the sides CA and CB respectively of ∆ABC, right angled at C. Prove that AE²+BD²=AB²+DE².

22. ABC and DBC are two ∆s on the same base BC and on the same side of BC with ÐA=ÐD=90⁰.If CA and   BD meet each other at E, show that AE x EC=BE x ED.

23. Prove that in a right angled triangle the square of hypotenuse is equal to the sum of the squares of the other two sides.

24. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that   the other two sides are divided into the same ratio.

25. ∆ ABC is right angled at B and D is midpoint of side BC. Prove that AC² = 4 AD² - 3 AB²

26. Prove that the ratio of the areas of two similar triangles is equal to the ratio of square of their corresponding sides.

27. In a ∆, if the square of one side is equal to sum of the squares of the other two sides, prove that the angle opposite to the first side is a right angle.

28. In an equilateral ∆ PQR, T is a point on the side QR, such that QT = QR. Prove that 9 PT² = 7 PQ²

29. P and Q are the mid points of side CA and CB respectively of ∆ ABC right angled at C. Prove that  4(AQ²+ BP²) = 5 AB².

30. CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC~∆PQR, prove that

(i) ∆AMC~∆PNR                  (ii) CM/RN=AB/PQ              (iii) ∆CMB~∆RNQ

31. The diagonal BD of a ||gm ABCD intersects the line segment AE at the point F, Where E is any point on the side BC. Prove that DF x EF=FB x FA.

32. Prove that three times the sum of the squares of the sides of a triangle is equal to  four times the sum of the squares of the medians of the triangle.

33. ABC is a right triangle with ÐA = 90⁰ ,A circle is inscribed in it. The lengths of the two sides containing the right angle are 6 cm and 8 cm. find the radius of the incircle. 

34. ABC is a right triangle, right angled at C. If  is the length of the perpendicular from C to AB and a, b, c  have the usual meaning, then prove that  cp=ab   

35. In a trapezium ABCD, AB||DC and DC=2AB.EF||AB, where E and F lie on the side BC and AD respectively such that BE/EC=4/3.Diagonal DB intersects EF at G. Prove that EF=11AB.

36. Sides AB, AC and median AD of a triangle ABC are respectively proportional to sides PQ, PR and median PM of another triangle PQR. Show that ∆ABC~∆PQR.