CBSE Guess > Papers > Important Questions > Class X > Maths > Mathematics By Mr. Sanjay Kumar

Chapter - 8

Q. 82. Two sides and a median bisecting one of these sides of a triangle are respectively proportional to the two sides and the corresponding median of the other triangle. Prove that the two triangles are similar.

Q. 83. In a triangle ABC, AD is perpendicular to the side BC and if BD/DA = DA/DC, prove that ABC is a right triangle.

Q. 84. ABC is a right triangle right-angled at B and the side BC is trisected at the points D and E such that the points B,D,E,C are in continuous manner. Prove that: 8 AE² = 3 AC² + 5 AD².

Q. 85. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Q. 86. The perpendicular from A to the side BC of a ∆ ABC intersects the side BC at D such that DB = 3 CD. Prove that: 2 AB² = 2 AC² + BC².

Q. 87. In a triangle ABC, DE // BC, BD : AB = 3:7. Find the ratio of the areas of the triangles ADE and ABC.

Q. 88. If one diagonal of a trapezium divides the other diagonal in the ratio 1:2, prove one of its parallel sides is double the other.

Q. 89. ABC is a triangle in which AB = AC and D is a point on AC such that BC² = AC × CD. Prove that ∆BCD is isosceles.

Q. 90. Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that: EL = 2 BL.

Q. 91. ABC is a triangle in which AB = AC and D is any point on side BC. Prove that: AB² - AD² = BD × CD.

Q. 92. ABC is a right triangle, right angled at C and AC = √3 BC. Find the measures of the angles A and B of ∆ABC.

Q. 93. In a triangle ABC, AD is a median. Prove that: AB² + AC² = 2AD² + 2 DC².

Q. 94. If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

Q. 95. In a ∆ PQR, PR = RQ and PQ² – QR² = PR². Determine all the three angles of the triangle.