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In Figure the line segment XY is parallel to side AC of ΔABC and it divides the triangle into two parts of equal areas. Find the ratio 𝐴𝑋/𝐵𝑋

ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2

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?

Two poles of height 6m and 11m stands on a plane ground, if the distance between their feet is 12m. Find the distance between their tops.

PQR is a triangle right-angled at P and M is a point on QR such that PM⊥QR. Show that PM2=QM×MR

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes

D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ABC. Find the ratio of the areas of ∆ DEF and ∆ ABC

AX and DY are altitudes of two similar triangles △ABC and △DEF Prove that AX DY=AB DE

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

Prove that the sum of the squares of the sides of rhombus is equal to the sum of the squares of its diagonals

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE2 CD2 = AC2 DE2

AX and DY are altitudes of two similar triangles △ABC and △DEF Prove that AX :DY=AB :DE

AB, CD, PQ are perpendicular to BD. AB = x, CD = y and PQ = z, prove that 1/ x 1 /y = 1/ z

Given that △ A B C ~ △ P Q R , CM and RN are respectively the medians of similar triangles △ A B C

A flag pole 4 m tall casts a 6 m shadow At the same time, a nearby building casts a shadow of 24 m

A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1 2 m s If the

The perimeters of two similar triangles are 30 cm and 20 cm respectively If one side of the first t

In △PQR PQR, ST is a line such thatProve that △PQR is an isosceles

Prove that the line joining the midpoints of any two sides of a triangle is parallel to the third si

Prove that a line drawn through the mid point of one side of a triangle parallel to another side bis

In given figure, If ∠ADE=∠CBA show that △ADE∼△ABC If AD=3 8cm,AE=3 6cm,BE=2 1cm and BC=4 2cm, find

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO.

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O.

In Fig. 6.21, A, B and C are points on OP, OQ, and OR respectively such that AB || PQ and AC || PR.

In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

In Fig. 6.19, DE || AC and DF || AE. Prove that BF/FE = BE/EC.

In Fig. 6.18, if LM || CB and LN || CD, prove that AM/AB = AN/AD

Find the zeroes of the quadratic polynomials 4x2−4x 1

The graphs of y = p(x) are given below for some polynomials p(x). Find the number of zeroes of p(x)