Question

Draw a right `DeltaABC` in which BC=12 cm, AB=5 cm, and `angleB=90^(@)`. Construct a triangle similar to it and of scale factor `(2)/(3)`. Is the new triangle also a right triangle ?

Answer 1

Steps of construction
1. Draw a line segment BC=12 cm.
2. From B draw a line AB=5 cm which makes right angle at B.

3. Join AC, `DeltaABC` is the given right triangle.
4. From B draw an acute `angleCBY` downwards.
5. On ray BY, mark three points `B_(1),B_(2) " and " B_(3)`, such that `BB_(1)=B_(1)B_(2)=B_(2)B_(3)`.
6. Join `B_(3)C`.
7. From point `B_(2)` draw `B_(2)N||B_(3)C` intersect BC at N.
8. From point N draw `NM||CA` intersect BA at M. `DeltaMBN` is the required triangle. `DeltaMBN` is also a right angled triangle at B.