In quadrilateral ABCD, AB=AD, AC bisects angleA . Prove DeltaABC~ADC .

In Delta ABC, AB = AC and AD is the angle bisector hat(A) meeting BC at D. If BD = 2.5 cm. Find BC.

ABCD is a quadrilateral in which AB= AD, the bisector of angle BAC and angle CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF || BD.

In Delta ABC , AB = AC and BC = 6cm, D is a point on the side AC such that AD = 5cm and CD = 4cm, show that Delta BCD ~ Delta ABC and hence find DB .

Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denotes the set of students and B denote the set of the sections. Define a relation from A to B as "x related to y if the student x belongs to the section y". Is this relation a function ? What can you say about the inverse relation ? Explain your answer.

In a quadrilateral ABCD, it is given that AB |\|CD and the diagonals AC and BD are perpendicular to each other. Show that AD.BC >= AB. CD .

In the adjacent figure, a line n falls on lines 1 and m such that the sum of the interior angles 1 and 2 is less than 180°, then what can you say about lines 1 and m.

Suppose that 120 are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as x related to y if the student x belongs to the section y. Is this relation a function? What can you say about the inverse relatioin. Explain your answer.

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = BC .

In a Delta ABC , AD is the bisector of angle A meeting side BC at D, if AB=10 cm, AC =14 cm and BC=6 cm, find BD and DC.