Advertisements
Advertisements
प्रश्न
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
उत्तर
Given that
AB2 = 2AC2
⇒ AB2 = AC2 + AC2
⇒ AB2 = AC2 + BC2 (As AC = BC)
The triangle is satisfying the pythagoras theorem
Therefore the given triangle is a right angle trangle
APPEARS IN
संबंधित प्रश्न
Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 7 cm, 24 cm, 25 cm
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.
Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?
