Show that \(\triangle\) PST~\(\triangle\) PQR 

Is \(\triangle\)ABC ~ \(\triangle\)PQR?

Observe Fig and find \(\angle\)P

\(\angle A=\angle CED\) prove that \(\Delta\ CAB \sim \Delta CED\) Also find the value of x.

QA and PB are perpendiculars to AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm. Find AQ.

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB

If \(\triangle\)ABC is similar to \(\triangle\)DEF such that BC = 3 cm, EF = 4 cm and area of \(\triangle\)ABC = 54 cm². Find the area of \(\triangle\)DEF.

Check whether the which triangles are similar and find the value of x.
(i)

(ii)

A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower.

Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT x TR = ST x TQ. \(\triangle\)

In the adjacent figure, \(\triangle\)ABC is right angled at C and DE\(\bot \) AB. Prove that \(\triangle\)ABC~\(\triangle\)ADE and hence find the lengths of AE and DE.

In the adjacent figure, \(\triangle\) ACB~\(\triangle\) APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

If figure OPRQ is a square and \(\angle\)MLN = 90^o. Prove that
\(\triangle\)LOP ~\(\triangle\)QMO

D and E are respectively the points on the sides AB and AC of a \(\triangle\)ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, show that DE || BC

In the figure, AD is the bisector of \(\angle\)A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

In the Figure, AD is the bisector of \(\angle\)BAC, if A = 10 cm, AC = 14 cm and BC = 6 cm. Find BD and DC.

ABCD is a trapezium in which AB || DC and P,Q are points on AD and BC respectively, such that PQ || DC if PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD.

In \(\triangle\)ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE||BC
AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.

In fig. if PQ || BC and PR ||CD prove that

 \(\frac { AB }{ AD } =\frac { AQ }{ AB } \)

In \(\triangle\)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

Check whether AD is bisector \(\angle\)A of \(\triangle\)ABC in each of the following AB = 5cm, AC = 10cm, BD = 1.5cm and CD = 3.5cm

An insect 8 m away initially from the foot of a lamp post which is 6 m tall, crawls towards it moving through a distance. If its distance from the top of the lamp post is equal to the distance it has moved, how far is the insect away from the foot of the lamp post?

What length of ladder is needed to reach a height of 7 ft along the wall when the base of the ladder is 4 ft from the wall? Round off your answer to the next tenth place.

A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?

In the rectangle WXYZ, XY+YZ = 17 cm, and XZ + YW = 26 cm .Calculate the length and breadth of the rectangle

The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.

Find the length of the tangent drawn from a point whose distance from the centre of a circle is 5 cm and radius of the circle is 3 cm.

In Figure, O is the centre of a circle. PQ is a chord and the tangent PR at P makes an angle of 50^o with PQ. Find \(\angle\)POQ,

In Fig, \(\triangle\) ABC is circumscribing a circle. Find the length of BC.

If radii of two concentric circles are 4 cm and 5 cm then find the length of the chord of one circle which is a tangent to the other circle

The length of the tangent to a circle from a point P, which is 25 cm away from the centre is 24 cm. What is the radius of the circle?

\(\triangle\) LMN is a right angled triangle with \(\angle\)L = 90^o. A circle is inscribed in it. The lengths of the sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.

A circle is inscribed in \(\triangle\)ABC having sides 8 cm, 10 cm and 12 cm as shown in figure, find AD, BE and CF.

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that \(\angle\)PQR = 120^o. Find \(\angle\)OPQ.

A tangent ST to a circle touches it at B. AB is a chord such that \(\angle\)ABT= 65^o. Find \(\angle\)AOB, where “O” is the centre of the circle.

In two concentric circles, a chord of length 16 cm of larger circle becomes a tangent to the smaller circle whose radius is 6 cm. Find the radius of the larger circle.

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q, such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

In the figure, if BD\(\bot \)AC and CE \(\bot \) AB, prove that
(i) \(\Delta AEC\sim \Delta ADB\)
(ii)  \(\frac { CA }{ AB } =\frac { CE }{ DB } \) 

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ b }^{ 2 }={ p }^{ 2 }+ax+\frac { { a }^{ 2 } }{ 4 } \)

Show that \(\triangle\)PST~\(\triangle\)PQR 

If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that

\(\triangle\)LOP~\(\triangle\)RPN

If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that

\(\triangle\)QMO ~\(\triangle\)RPN

If figure OPRQ is a square and \(\angle\)MLN = 90^o. Prove that

QR² = MQ x RN

In fig. if PQ || BC and PR || CD prove that

\(\frac { QB }{ AQ } =\frac { DR }{ AR } \)

Check whether AD is bisector \(\angle\)A of \(\triangle\)ABC in each of the following AB = 4cm, AC = 6cm, BD = 1.6cm and CD = 2.4cm.

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ c }^{ 2 }={ p }^{ 2 }-ax+\frac { { a }^{ 2 } }{ 4 } \)

D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
\({ b }^{ 2 }+{ c }^{ 2 }={ 2p }^{ 2 }+\frac { { a }^{ 2 } }{ 2 } \)

Are square and a rhombus similar or congruent. Discuss.

Are a rectangle and a parallelogram similar. Discuss.

Are any two right angled triangles similar? If so why?

Give two different examples of pair of non-similar figures?

Write down any five Pythagorean triplets?

Can all the three sides of a right angled triangle be odd numbers? Why?

Can we draw two tangents parallel to each other on a circle?

Can we draw two tangents perpendicular to each other on a circle?