Draw a right triangle ABC in which $B C = 12 cm$ , $A B = 5 cm$ and $∠ B = 90 °$ . Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle?

Open in App

Solution

Draw the required diagram with the help of the given statement.
The steps of construction are outlined below:
Draw a line segment with the length $A B = 5 cm$ . At point $A$ , build a right angle $A B C$ .
To intersect $C A$ at $C$ , draw an arc with a radius of $12 cm$ with $B$ as its centre.
Join $B C$ in order to get $A B C$ .
Draw a ray $A X$ opposite to vertex $C$ that forms an acute angle with $A B$ .
Find three points $A_{1}, A_{2}, A_{3}$ on line segment $A X$ , such that $A A_{1} = A A_{2} = A A_{3}$ .
Join $B A_{3}$ .
Draw a line parallel to $B A_{3}$ through $A_{2}$ , intersecting $A B$ at $B'$ .
Draw a line parallel to $B C$ through $B'$ , intersecting $A C$ at $C'$ .
The required triangle is the $A B' C'$ triangle as shown below:
Hence, the required diagram is shown below:

Suggest Corrections

Similar questions

Question 3
Draw a $Δ$ ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$ .
Thinking process
Here, scale factor = $\frac{m}{n} = \frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

Q. Draw a right triangle ABC in which

B C = 12 cm

cm,

A B = 5 cm

cm and

∠ B = 90^{\circ} .

Construct a triangle similar to it and of scale factor

\frac{2}{3}

. Is the new triangle also a right triangle?

Question 2
Draw a right $Δ$ ABC in which BC = 12 cm AB = 5 cm and $∠ B = 90^{\circ}$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle?
Thinking process
Here scale factor $\frac{m}{n} = \frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

Question 2
Draw a right $Δ$ ABC in which BC = 12 cm AB = 5 cm and $∠ B = 90^{\circ}$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle?
Thinking process
Here scale factor $\frac{m}{n} = \frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

Q. Construct a triangle similar to

△ A B C

in which

A B = 4.6 c m, B C = 5.1 c m,

(∠ A) = 60^{o}

with scale factor

4 : 5

Join BYJU'S Learning Program

Draw a right triangle ABC in which BC=12cm, AB=5cm and ∠B=90°. Construct a triangle similar to it and of scale factor 23. Is the new triangle also a right triangle?

Draw a right triangle ABC in which $B C = 12 cm$ , $A B = 5 cm$ and $∠ B = 90 °$ . Construct a triangle similar to it and of scale factor $\frac{2}{3}$ . Is the new triangle also a right triangle?