Similar Triangles - 10th Class - Worksheet1- English Medium - 20MCQ's-Telangana

Chapter 8: Similar Triangles

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1. If \(\triangle ABC \sim \triangle PQR\), which of the following ratios is correct?

• A) \(\frac{AB}{PQ} = \frac{BC}{PR} = \frac{AC}{QR}\)
• B) \(\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}\)
• C) \(\frac{AB}{QR} = \frac{BC}{PQ} = \frac{AC}{PR}\)
• D) \(\frac{AB}{PR} = \frac{BC}{QR} = \frac{AC}{PQ}\)

2. All congruent figures are similar, but similar figures are:

• A) Always congruent
• B) Never congruent
• C) Not necessarily congruent
• D) Equal in area

3. In \(\triangle XYZ\), \(ST \parallel YZ\) with \(S\) on \(XY\) and \(T\) on \(XZ\). If \(XS = 3\text{ cm}\), \(SY = 6\text{ cm}\), and \(XT = 4\text{ cm}\), find the length of \(XZ\).

• A) \(8\text{ cm}\)
• B) \(12\text{ cm}\)
• C) \(9\text{ cm}\)
• D) \(10\text{ cm}\)

4. In \(\triangle LMN\), a line \(PQ\) cuts \(LM\) at \(P\) and \(LN\) at \(Q\) such that \(\frac{LP}{PM} = \frac{LQ}{QN}\). Which theorem justifies that \(PQ \parallel MN\)?

• A) Pythagoras Theorem
• B) Basic Proportionality Theorem (Thales Theorem)
• C) Converse of Basic Proportionality Theorem
• D) AAA Similarity Criterion

5. Two triangles are similar if their corresponding angles are equal. This is known as which criterion?

• A) SSS
• B) SAS
• C) AAA
• D) RHS

6. If in \(\triangle DEF\) and \(\triangle PQR\), \(\frac{DE}{PQ} = \frac{EF}{QR}\) and \(\angle E = \angle Q\), then the triangles are similar by which criterion?

• A) SSS
• B) SAS
• C) AAA
• D) RHS

7. In two similar triangles \(\triangle ABC\) and \(\triangle DEF\), the ratio of their corresponding sides is \(3:5\). What is the ratio of their areas?

• A) \(3:5\)
• B) \(6:10\)
• C) \(9:25\)
• D) \(27:125\)

8. If the areas of two similar triangles are in the ratio \(81:49\), then the ratio of their corresponding altitudes is:

• A) \(9:7\)
• B) \(81:49\)
• C) \(3:7\)
• D) \(7:9\)

9. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This statement is known as:

• A) Thales Theorem
• B) Mid-point Theorem
• C) Pythagoras Theorem
• D) Apollonius Theorem

10. Which of the following sets of side lengths forms a right-angled triangle?

• A) \(5\text{ cm}, 7\text{ cm}, 9\text{ cm}\)
• B) \(6\text{ cm}, 8\text{ cm}, 10\text{ cm}\)
• C) \(4\text{ cm}, 5\text{ cm}, 6\text{ cm}\)
• D) \(3\text{ cm}, 4\text{ cm}, 6\text{ cm}\)

11. A man travels \(12\text{ m}\) due West and then \(5\text{ m}\) due North. How far is he from his starting point?

• A) \(17\text{ m}\)
• B) \(7\text{ m}\)
• C) \(13\text{ m}\)
• D) \(15\text{ m}\)

12. In \(\triangle ABC\), \(\angle B = 90^\circ\) and \(BD \perp AC\). If \(AD = 4\text{ cm}\) and \(DC = 9\text{ cm}\), what is the length of \(BD\)?

• A) \(6\text{ cm}\)
• B) \(5\text{ cm}\)
• C) \(13\text{ cm}\)
• D) \(36\text{ cm}\)

13. In an equilateral triangle of side \(2a\), the length of each altitude is:

• A) \(a\sqrt{2}\)
• B) \(a\sqrt{3}\)
• C) \(2a\sqrt{3}\)
• D) \(\frac{a\sqrt{3}}{2}\)

14. If a line divides any two sides of a triangle in the same ratio, then the line must be:

• A) Perpendicular to the third side
• B) Parallel to the third side
• C) Equal to half the third side
• D) Bisecting the third side

15. If \(\triangle ABC \sim \triangle DEF\), \(\text{Area}(\triangle ABC) = 64\text{ cm}^2\), \(\text{Area}(\triangle DEF) = 121\text{ cm}^2\), and \(EF = 11\text{ cm}\), find \(BC\).

• A) \(8\text{ cm}\)
• B) \(6.4\text{ cm}\)
• C) \(11\text{ cm}\)
• D) \(8.8\text{ cm}\)

16. Vertical poles of heights \(6\text{ m}\) and \(11\text{ m}\) stand vertically on a plane ground. If the distance between their feet is \(12\text{ m}\), what is the distance between their tops?

• A) \(13\text{ m}\)
• B) \(14\text{ m}\)
• C) \(15\text{ m}\)
• D) \(17\text{ m}\)

17. If \(\triangle ABC\) is an isosceles right triangle right-angled at \(C\), then \(AB^2 =\)

• A) \(AC^2\)
• B) \(2AC^2\)
• C) \(3AC^2\)
• D) \(4AC^2\)

18. A vertical stick \(1.8\text{ m}\) long casts a shadow \(1.2\text{ m}\) long on the ground. At the same time, a tower casts a shadow \(24\text{ m}\) long. What is the height of the tower?

• A) \(36\text{ m}\)
• B) \(16\text{ m}\)
• C) \(32\text{ m}\)
• D) \(40\text{ m}\)

19. In \(\triangle ABC\), \(D\) and \(E\) are points on sides \(AB\) and \(AC\) respectively such that \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\), and \(EC = x - 1\), find the value of \(x\).

• A) \(3\)
• B) \(4\)
• C) \(5\)
• D) \(6\)

20. The perimeter of two similar triangles \(\triangle ABC\) and \(\triangle PQR\) are \(30\text{ cm}\) and \(20\text{ cm}\) respectively. If \(AB = 12\text{ cm}\), find the corresponding side \(PQ\).

• A) \(6\text{ cm}\)
• B) \(8\text{ cm}\)
• C) \(10\text{ cm}\)
• D) \(9\text{ cm}\)