CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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3 Mark Questions

Question 1:

In each of the following, give the justification of the construction also:

Draw a line segment of length and divide it in the ratio . Measure the two parts.

Given: A line segment of length .

To construct: To divide it in the ration and to measure the two parts.

Steps of construction:

(a) From any ray AX, making an acute angle with AB.

(b) Locate points and on AX such that

(c) Join

(d) Through the point , draw a line parallel to intersecting AB at the point C.

Then,

On measurement, ,

Justification:

[By construction]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

Question 2:

Construct a triangle of sides , and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle

To construct: To construct a triangle of sides , and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.

Steps of construction:

(a) Draw a triangle of sides , and .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate points and on such that .

(d) Join and draw a line through the point B2, draw a line parallel to intersecting BC at the point C ′ .

(e) Draw a line through C ‘parallel to the line CA to intersect BA at A’ .

Then, A ‘BC’ is the required triangle.

Justification:

[By construction]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

[By construction]

[AA similarity]

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