Question

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and B = 90º. Construct a triangle similar to it and of

scale factor 2/3 . Is the new triangle also a right triangle?​

Answer 1

Step-by-step explanation:

In ΔABC,

AB=5 cm, BC=12 cm, ∠B=90

o

To construct-

A Δ of scale factor =

3

2

Construction- BC is divided into ratio 2:3 at D.

DE drawn AB.

It intersects AC at E.

ΔDEC is the desired Δ.

To find out- ΔABC and ΔEDC are similar or not.

Solution-

Between ΔABC and ΔEDC, we have AB∥ED ....(by\quad Construction)

∴∠ABC=∠EDC ....(corresponding\quad angles)

and ∠ACB is common.

∴ΔABC and ΔEDC are similar

Answer 2

Answer:

In ΔABC, 

AB=5 cm,  BC=12 cm, ∠B=90o

To construct-

A Δ of scale factor =32 

Construction- BC is divided into ratio 2:3 at D.

DE drawn AB.

It intersects AC at E.

ΔDEC is the desired Δ.

To find out- ΔABC and ΔEDC are similar or not.

Solution-

Between ΔABC and ΔEDC, we have AB∥ED     ....(by\quad Construction)

∴∠ABC=∠EDC      ....(corresponding\quad angles)

and ∠ACB is common. 

∴ΔABC and ΔEDC are similar.

Ans- Yes

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