Page 56 - Mathematics Class - X

Viva-Voce

1. State the Basic Proportionality Theorem.
Ans. BPT states that “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same ratio”.
2. Who gave theorem?
Ans. Basic proportionality theorem also known as Thales Theorem was given by the Greek Mathematician Thales.
3. Is the converse of the basic proportionality theorem true? If yes, state it.
Ans. Yes! The converse of the basic proportionality theorem is also true and it states that “If a line divides any
two sides of a triangle in the same ratio, the line is parallel to the third side of the triangle.”

4. A line parallel to one side of a triangle divides the other side in the ratio 3: 5. In what ratio will the third side
be divided?

Ans. According to Thales Theorem it will divide the other side in the same ratio, i.e., 3:5.
5. Is Basic Proportionality Theorem true for any two equiangular triangles?
Ans. Yes! The BPT is true for all types of triangles.

MCQs

1. ΔABC ~ ΔPQR. If ar (∆ABC) = 2.25 m , ar (∆PQR) = 6.25 m , PQ = 0.5 m, then length of AB is
2
2
a) 30 cm b) 0.5 m c) 50 cm d) 3 m
2. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm,
BD = 4 cm, BC = 9 cm and DE || BC. Then, length of DE (in cm) is
a) 6 b) 5 c) 3 d) 2.5
3. If the ratio of the corresponding sides of two similar triangles is 2 : 3, then the ratio of their corresponding
altitude is

a) 3 : 2 b) 16 : 81 c) 4 : 9 d) 2 : 3
4. Lance the alien is 5 feet tall. His shadow is 8 feet long.
[1 feet = 12 inches]
At the same time of day, a tree’s shadow is 32 feet long.
What is the height of the tree?
a) 20 feet b) 24 feet
c) 29 feet d) 51 feet

5. In the given figure, the two triangles are similar. What is the value of x?
a) 12.4
b) 13.2
c) 14

d) 18.6

Answers: 1. a) 30 cm 2. c) 3 3. c) 2 : 3 4. a) 20 feet 5. b) 13.2

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