NCERT Class 10 Maths — Chapter 6

Exercise 6.2: Basic Proportionality Theorem (BPT)

Use the Basic Proportionality Theorem (if a line is parallel to one side of a triangle, it divides the other two sides proportionally) to solve problems.

BPTThales theoremparallel line dividing sides proportionally

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Extra Practice Questions

These questions cover the same concepts as Exercise 6.2. Try solving them to build confidence before or after the textbook exercise.

If ΔABC ~ ΔPQR, and AB/PQ = 3/5. If the perimeter of ΔABC is 36 cm, what is the perimeter of ΔPQR?

A.A. 21.6 cm

B.B. 60 cm

C.C. 45 cm

D.D. 72 cm

In ΔABC, D and E are points on sides AB and AC respectively such that DE || BC. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, find the value of x.

A.A. 2

B.B. 3

C.C. 4

D.D. 5

Given two triangles, ΔABC and ΔXYZ. If AB/XY = BC/YZ = CA/ZX = k, and k = 1, then the triangles are congruent. If k ≠ 1, the triangles are similar. Which of the following statements about SSS similarity is always true?

A.If the perimeters of ΔABC and ΔXYZ are equal, then k must be 1.

B.If the areas of ΔABC and ΔXYZ are equal, then k must be 1.

C.If k = 2, then the altitude from A to BC is twice the altitude from X to YZ.

D.All of the above.

A ladder 15 m long is placed against a wall such that its foot is 9 m away from the wall. If the top of the ladder slips down by 3 m, how much further will its foot slide away from the wall?

A.3 m

B.4 m

C.5 m

D.6 m

Which of the following conditions is essential for applying the Pythagoras Theorem to a triangle?

A.The triangle must be equilateral.

B.The triangle must be a right-angled triangle.

C.The triangle must be isosceles.

D.The triangle must be acute-angled.

If two triangles are similar, and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

A.2:3

B.4:9

C.8:27

D.1:1 (equal areas)

Two figures are said to be similar if they have the same shape but not necessarily the same size. Which of the following pairs of figures are ALWAYS similar?

A.Two rectangles.

B.Two triangles.

C.Two squares.

D.Two quadrilaterals.

In a right-angled triangle PQR, right-angled at Q, if QS ⊥ PR, and PQ = 6 cm, QR = 8 cm. What is the ratio of the area of ΔPQS to the area of ΔRQS?

A.9:16

B.3:4

C.16:9

D.4:3

Two triangles ΔXYZ and ΔMNO have sides such that XY = 4 cm, YZ = 6 cm, ZX = 8 cm and MN = 6 cm, NO = 9 cm, OM = 12 cm. Are these triangles similar?

A.A. Yes, by SSS similarity

B.B. No, they are not similar