Question

triangle PQR is constructed similar to triangle ABC with scale factor. triangle PQR is​

Answer 1

Anwer: triangle PQR is Similar to triangleABC

Answer 2

$\triangle PQR$ is the required triangle which is similar to $\triangle ABC$.

Step-by-step explanation:

Given,

$\triangle PQR$ is constructed similar to $\triangle ABC$ with scale factor.

Scale Factor:

In two similar geometric figures, the ratio of their corresponding sides is called the scale factor.

Take a $\triangle ABC$ which is Equilateral triangle where all sides and all angles are equal as shown in the figure.

Now,

For $\triangle PQR$,

$PQ=2AB,QR=2BC\ and\ QR=2CA$

Also, $\angle A=\angle P=\angle B=\angle Q=\angle C=\angle R=60\ degree$

Following steps:

• Draw a line segments $QR=2BC$ using scale.
• At $Q$, draw an angle $60\ degree$ using protector like $\angle RQX=60\ degree$
• Also at $R$, draw an angle $60\ degree$ using protector like $\angle QRY=60\ degree$
• Where line $QX\ and\ RY$ intersect at $P$

Hence, $\triangle PQR$ is the required triangle which is similar to $\triangle ABC$.