CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 14 (For CBSE, ICSE, IAS, NET, NRA 2022)
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Question 24:
Draw a triangle ABC with side , , . Then construct a triangle whose sides are times the corresponding sides of .
Answer:
To construct: To construct a triangle ABC with side , and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.
Steps of construction:
(a) Draw a triangle ABC with side , and .
(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.
(c) Locate 4 points and on BX such that .
(d) Join B3C and draw a line through the point , draw a line parallel to intersecting BC at the point C ′ .
(e) Draw a line through parallel to the line to intersect BA at A. ′
Then, A ‘BC’ is the required triangle.
Justification
[By construction]
[AA similarity]
[By Basic Proportionality Theorem]
But [By construction]
Therefore,
[By construction]
[AA similarity]
[From eq. (i) ]
Question 25:
Draw a right triangle in which the sides (other than hypotenuse) are of lengths and . Then construct another triangle whose sides are times the corresponding sides of the given triangle
Answer:
To construct: To construct a right triangle in which sides (other than hypotenuse) are of lengths and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.
Steps of construction:
(a) Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and .
(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.
(c) Locate 5 points and on BX such that .
(d) Join and draw a line through the point , 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]
[AA similarity]
[By Basic Proportionality Theorem]
But [By construction]
Therefore,
[By construction]
[AA similarity]
[From eq. (i) ]