Class 10 Mathematics Part 2 (Geometry) – Chapter 1: Similarity MCQ
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Triangles ABC and PQR have equal heights. If BC = 8 cm and QR = 12 cm, what is A(ΔABC) : A(ΔPQR)?
Chapter 1: Similarity
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Answer: C. 2 : 3
With equal heights, areas are in the ratio of the bases: 8 : 12 = 2 : 3.Two triangles have equal bases and their heights are 5 cm and 7 cm. What is the ratio of their areas?
Chapter 1: Similarity
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Answer: A. 5 : 7
With equal bases, areas are in the ratio of the corresponding heights: 5 : 7.In ΔABC, a line parallel to BC meets AB at D and AC at E. If AD = 3, DB = 6 and AE = 4, find EC.
Chapter 1: Similarity
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Answer: D. 8
By the basic proportionality theorem AD/DB = AE/EC, so 3/6 = 4/EC and EC = 8.A line cuts two sides of a triangle in distinct points and divides them in the same ratio. What can we conclude about this line?
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Answer: B. It is parallel to the third side
This is the converse of the basic proportionality theorem: such a line is parallel to the third side.In ΔPQR, ray PS bisects ∠QPR and meets QR at S. If PQ = 6, PR = 9 and QS = 4, find SR.
Chapter 1: Similarity
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Answer: C. 6
By the angle bisector theorem PQ/PR = QS/SR, so 6/9 = 4/SR and SR = 6.What does the SAS test of similarity require?
Chapter 1: Similarity
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Answer: B. Two pairs of corresponding sides in the same ratio and the included angles equal
SAS similarity: the ratios of two pairs of corresponding sides are equal and the angles included between them are equal.ΔABC ~ ΔPQR and AB : PQ = 3 : 5. What is A(ΔABC) : A(ΔPQR)?
Chapter 1: Similarity
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Answer: D. 9 : 25
Areas of similar triangles are in the ratio of the squares of corresponding sides: 3² : 5² = 9 : 25.ΔABC ~ ΔPQR, A(ΔABC) : A(ΔPQR) = 16 : 25 and AB = 8 cm. Find PQ.
Chapter 1: Similarity
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Answer: A. 10 cm
Side ratio = √16 : √25 = 4 : 5, so 8/PQ = 4/5 and PQ = 10 cm.Three parallel lines make intercepts AB = 4 and BC = 6 on one transversal and PQ = 6 and QR on another. Find QR.
Chapter 1: Similarity
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Answer: D. 9
Intercepts made by three parallel lines are proportional: 4/6 = 6/QR, so QR = 9.In ΔABC, ∠A = 50° and ∠B = 60°. In ΔPQR, ∠P = 50° and ∠R = 70°. Which statement is correct?
Chapter 1: Similarity
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Answer: A. ΔABC ~ ΔPQR by the AA test
∠C = 70° and ∠Q = 60°, so A↔P, B↔Q, C↔R; two pairs of equal angles give ΔABC ~ ΔPQR (AA).
All questions are written by PadhaiNotes in our own words from this chapter of the official Maharashtra State Board Balbharati textbook.