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A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.

Solution Let the length of the ladder = AC = 5 m Let the height of the wall on which ladder is placed = BC = 4m. From right-angled ∆EBD, On... View Article

In Fig 6.17, if PQRS is a parallelogram and AB||PS, then prove that OC||SR.

Given According to the given details PQRS is a parallelogram, Therefore, PQ || SR and PS || QR. Also given, AB || PS. To prove: OC... View Article

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Answer Given ∆ABC in which a line DE parallel to BC intersects AB at D and AC at E. To prove DE divides the two sides in the same... View Article

It is given that ∆ ABC ~ ∆ EDF such that AB = 5 cm, AC = 7 cm, DF= 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

Solution: According to the given details ∆ABC ∼ ∆EDF From the property of a similar triangle, We know that the... View Article

In Fig. 6.16, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

Solution: According to the given data ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm CP = 4 cm From ∆APB and ∆CPD, ∠A... View Article

If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.

Solution: According to the given details AB = 4 cm, DE = 6 cm EF = 9 cm FD = 12 cm Also, ∆ABC ∼ ∆DEF Hence On... View Article

Find the altitude of an equilateral triangle of side 8 cm.

Solution Let us consider ABC as an equilateral triangle of side 8 cm AB = BC = CA = 8 cm. (All sides of an equilateral triangle is equal)... View Article

In figure, if AB || DC and AC, PQ intersect each other at the point O. Prove that OA.CQ = 0C.AP.

Solution According to the given details AC and PQ intersect each other at the point O and AB||DC. From ∆AOP and ∆COQ, ∠AOP... View Article

Diagonals of a trapezium PQRS intersect each other at the point 0, PQ || RS and PQ = 3 RS. Find the ratio of the areas of Δ POQ and Δ ROS.

Solution According to the given data PQRS is a trapezium in which PQ‖RS and PQ = 3RS PQ/RS = 3/1 = 3 …(i) From ∆POQ and ∆ROS,... View Article

In figure, if ∠1 =∠2 and ΔNSQ = ΔMTR, then prove that ΔPTS ~ ΔPRQ.

Solution According to the given data we get to know that ∆ NSQ ≅ ∆MTR ∠1 = ∠2 Since, ∆NSQ = ∆MTR So, SQ = TR... View Article

Find the value of x for which DE||AB in given figure.

Solution: According to the given details DE || AB Using the basic proportionality theorem, we obtain CD/AD = CE/BE ∴ When... View Article

In a ΔPQR, PR² – PQ²= QR² and M is a point on side PR such that QM ⊥ PR. Prove that QM² =PM × MR.

Solution According to the given data, in ∆PQR, PR2 = QR2 and QM⊥PR On applying the Pythagoras theorem, we get... View Article

Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.

Answer The given statement is false Two quadrilaterals will be similar if their corresponding angles are equal and the ratio of their... View Article

In ΔPQR and ΔMST, ∠P = 55°, ∠Q =25°, ∠M = 100° and ∠S = 25°. Is ΔQPR ~ ΔTSM? Why?

Solution We know that, The sum of the three angles of a triangle = 180°. From ∆PQR, ∠P + ∠Q + ∠R = 180°... View Article

In figure, BD and CE intersect each other at the point P. Is ΔPBC ~ ΔPDE? Why?

Answer The given statement is True. Solution From ∆PBC and ∆PDE, ∠BPC = ∠EPD [vertically opposite angles] PB/PD =... View Article

A and B are respectively the points on the sides PQ and PR of a ΔPQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reason for your answer.

Answer The given statement is True. Solution PQ = 12.5 cm PA = 5 cm BR = 6 cm PB = 4 cm So QA = QP – PA = 12.5 – 5 =... View Article

It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P ? Why?

Answer The given statement is False. Solution We know that, The corresponding angles are equal in similar triangles. So, ∠D... View Article

Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reason for your answer.

Answer The given statement is False. Solution According to the given details, Let us consider A = 25 cm B = 5 cm C = 24 cm On... View Article

In figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to (a) 50° (b) 30° (c) 60° (d) 100°

Answer The correct answer is (d) 100° Solution From ∆APB and ∆CPD, ∠APB = ∠CPD = 50° (since they are vertically... View Article

If in two Δ PQR,AB/QR = BC/PR = CA/PQ, then (a)Δ PQR~Δ CAB (b) Δ PQR ~ Δ ABC (c)Δ CBA ~ Δ PQR (d) Δ BCA ~ Δ PQR

Answer The correct answer is (a)Δ PQR~Δ CAB Solution From ∆ABC and ∆PQR, we know that AB/QR = BC/PR = CA/PQ Also, sides of one... View Article

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