wiz-icon
MyQuestionIcon
MyQuestionIcon
12
You visited us 12 times! Enjoying our articles? Unlock Full Access!
Question

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. the construct another triangle whose sides are times the corresponding sides of the given triangle. Give the justification of the construction.

Open in App
Solution

It is given that sides other than hypotenuse are of lengths 4 cm and 3 cm. Clearly, these will be perpendicular to each other.

The required triangle can be drawn as follows.

Step 1

Draw a line segment AB = 4 cm. Draw a ray SA making 90° with it.

Step 2

Draw an arc of 3 cm radius while taking A as its centre to intersect SA at C. Join BC. ΔABC is the required triangle.

Step 3

Draw a ray AX making an acute angle with AB, opposite to vertex C.

Step 4

Locate 5 points (as 5 is greater in 5 and 3), A1, A2, A3, A4, A5, on line segment AX such that AA1 = A1A2 = A2A3 = A3A4 = A4A5.

Step 5

Join A3B. Draw a line through A5 parallel to A3B intersecting extended line segment AB at B'.

Step 6

Through B', draw a line parallel to BC intersecting extended line segment AC at C'. ΔAB'C' is the required triangle.

Justification

The construction can be justified by proving that

In ΔABC and ΔAB'C',

∠ABC = ∠AB'C' (Corresponding angles)

∠BAC = ∠B'AC' (Common)

∴ ΔABC ∼ ΔAB'C' (AA similarity criterion)

… (1)

In ΔAA3B and ΔAA5B',

∠A3AB = ∠A5AB' (Common)

∠AA3B = ∠AA5B' (Corresponding angles)

∴ ΔAA3B ∼ ΔAA5B' (AA similarity criterion)

On comparing equations (1) and (2), we obtain

This justifies the construction.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Incenter and Construction of Incircle in a Triangle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon