**KSEEB SSLC Solutions for Class 10 Maths – Similar Triangles (English Medium)**

**Exercise 10.1:**

**Question 1:**

In the given pairs of similar triangles, write the corresponding vertices, corresponding sides and their ratios.

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**Question 2:**

Study the following figures and find out in each case whether the triangles are similar. Given reason.

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**Question 3(i):**

Find the unknown values in each of the following figure. All lengths are given in centimeters. (Measures are not to scale)

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**Question 3(ii):**

Find the unknown values in each of the following figures. All lengths are given in centimeters. (Measures are not to scale)

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**Question 3(iii):**

Find the unknown values in each of the following figures. All lengths are given in centimeters. (Measures are not to scale)

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**Question 4:**

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**Question 5:**

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**Question 6:**

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**Question 7:**

In the given figure, AE ll DB, BC = 7cm, BD = 5cm, DC = 4cm. If CE = 12 cm, find AE and AC.

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**Question 8:**

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**Question 9:**

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**Question 10:**

A vertical pole of 10 m casts a shadow of 8 m at certain time of the day. What will be the length of the shadow cast by the tower standing next to the pole, if its height is 110 m?

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**Question 11:**

A ladder resting against a vertical wall has its foot on the ground at a distance of 6 cm from the wall. A man on the ground climbs two-thirds of the ladder. What will be his distance from the wall now?

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**Exercise 10.2:**

**Question 1:**

Study the adjoining figure. Write the ratios in relation to basic proportionality theorem and its corollaries, in terms of a, b, c and d.

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**Question 2:**

In the adjoining figure DE ll AB, AD = 7cm, CD = 5cm and BC = 18 cm. Find BE and CE.

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**Question 3:**

In ΔABC, D and E are points on the sides AB and AC respectively such that DE ll BC.

- If AD = 6cm, DB = 9cm and AE = 8cm, Find AC.
- If AD = 8cm, AB =12 cm, AE = 12 cm, find CE.
- If AD = 4x – 3, BD = 3x – 1, AE = 8x – 7, and CE = 5x – 3 find the value x.

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**Question 4:**

In the figure, PQ ll BC AP = 3cm, AR = 4.5 cm, AQ = 6 cm, AB = 5cm and AC = 10 cm. Find the lengths of AD.

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**Question 5:**

In ΔPQR, E and F are points on the sides PQ and PR respectively. For each other of the following cases, verify EF ll QR

i. PE = 3.9 cm, EQ = 3cm, PF = 3.6 cm, FR = 2.4 cm

ii. PE = 4 cm, QE = 4.5 cm, PF = 8cm, FR = 9cm

iii. PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm

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**Question 6:**

Which of the following sets of data make FG ll BC?

i. AB = 14cm, AF = 6cm, AC = 7cm, AG = 3cm

ii. AB = 12 cm, FB = 3cm, AC = 8cm, AG = 6cm

iii. AF = 6cm, FB = 5cm, AG = 9cm, GC = 8cm

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**Question 7:**

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**Question 8:**

In the adjoining figure, AC ll BD and CE ll DF.

If OA = 12 cm, AB = 9cm, OC = 8cm and EF = 4.5 cm, find OE.

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**Question 9:**

In the figure PC ll QK and BC ll HK. If AQ = 6cm. QH = 4 cm, HP = 5cm and KC = 18 cm, find AK and PB.

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**Question 10:**

At a certain time of the day a tree casts its shadow 12.5 feet long. If the height of the tree is 5 feet, find the height of another tree that casts its shadow 20 feet long at the same time.

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**Exercise 10.3:**

**Question 1:**

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**Question 2:**

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**Question 3:**

State ‘Mid point Theorem’. Prove the theorem using ‘Converse of Thale’s Theorem.

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Mid point theorem : “In any triangle the line joining the midpoints of any two sides of a triangle is parallel to the third side and half the third side”.

**Question 4:**

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**Question 5:**

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**Question 6:**

ABCD is a quadrilateral in which W, X, Y and Z are the points of trisection of sides AB, BC, CD and DA respectively. Prove that WXYZ is a parallelogram.(Hint : Join A,C)

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**Question 7:**

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**Question 8:**

In ∆ABC, PQ ll BC and BD = DC Prove that PE ll EQ (Note : In ∆ABC, median AD bisects the line which is parallel to BC).

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**Question 9:**

In the figure, PR ll BC and QR ll BD Prove that PQ ll CD

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**Question 10:**

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**Exercise 10.4:**

**Question 1:**

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**Question 2:**

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**Question 3:**

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**Question 4:**

If the diagonals of quadrilateral divide each other proportionally then prove that the quadrilateral is a trapezium.

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**Question 5:**

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**Question 6:**

The diagonal BD of a ll^{gm} ABCD intersects AE at ‘F’. ‘E’ is any point on BC. Prove that DF.EF = FB. FA

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**Question 7:**

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**Question 8:**

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**Question 9:**

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**Question 10:**

If the mid points of three sides of a triangle are joined in an order, then prove that the four triangles so formed are similar to each other and to the original triangle.

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**Exercise 10.5:**

**Question 1(i):**

In which of the following cases the pairs of triangles are similar?

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(ii):**

In which of the following cases the pairs of triangles are similar?

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(iii):**

In which of the following cases the pairs of triangles are similar?

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(iv):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(v):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(vi):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(vii):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(viii):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(ix):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Question 1(x):**

Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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**Exercise 10.6:**

**Question 1:**

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**Question 2:**

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**Question 3:**

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**Question 4:**

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**Question 5:**

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**Exercise 10.7:**

**Question 1:**

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**Question 2:**

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**Question 3:**

Two isosceles triangles are having equal vertical angles and their areas are in the ratio 9 : 16. Find the ratio of their corresponding altitudes.

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**Question 4:**

The corresponding altitudes of two similar triangles are 3 cm and 5 cm respectively. Find the ratio between their areas.

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**Question 5:**

In the trapezium ABCD, AB ll CD, AB = 2CD and ar (∆AOB)= 84cm^{2}, find the area of ∆COD

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**Question 6:**

In the figure (trapezium ABCD, AB ll CD, AB = 2CD), find the ratios between areas of ∆AOB and ∆COD, if AB = 3 CD.

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**Question 7:**

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

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