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.
| Chapter 1 | Chapter 2 | Chapter 3 |
| Chapter 4 | Chapter 5 | Chapter 6 |
| Chapter 7 | Chapter 8 | Chapter 9 |
| Chapter 10 | Chapter 11 | Chapter 12 |
| Chapter 13 | Chapter 14 | Chapter 15 |
| Chapter 16 |
