Choose whether the given statement is true or false.

A triangle of sides 4 cm, 5cm, and 6cm and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle can be constructed.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let us first draw the triangle with sides 4 cm, 5cm and 6cm.
- First, we will draw the base AB of the triangle of length 4cm.
- Then draw an arc of 5cm from A.
- Similarly, draw an arc of 6cm from B.
- Finally we will mark the point of intersection as C and then join the points A and C and A and B.

https://www.vedantu.com/question-sets/d5fa0431-f625-4a11-87ff-25c101aa882c5790501685588017648.png

Now we will construct a similar triangle of ABC whose sides are

\frac{2}{3}

of the corresponding sides of ΔABC.
We will first draw a line AY such that it makes an acute angle with line AB on the opposite side of vertex C.

https://www.vedantu.com/question-sets/016a55b4-95eb-4d63-b17b-bc10770cdb165243886319545948795.png

Now we will mark three points at equal distances from each other on the line AY i.e. AA1 = A1A2 = A2 A3

https://www.vedantu.com/question-sets/57eff303-53f0-4622-a1d3-68d8044b92f48078369909074001097.png

Now we will join A3 to B and then we will draw a parallel line A2B′ to the line AB such that it intersect AB at B′.

https://www.vedantu.com/question-sets/5ad5267a-9b10-4ffe-9509-a76ee604feda377744717927156992.png

Now we will finally draw a line from B′ to AC such that it intersects AC at C′ and the line B′C′ is parallel to the line BC.
Hence, the given statement is true.

Watch 3-min video & get full concept clarity