Question

Construct a right-angled `Delta ABC` in which `angleA=90^(@)`, hypotenuse `BC=6` cm and `AB=4` cm. Justify your construction.

Answer 1

STEPS OF CONSTRUCTION
(i) Draw a line segment `BC=6` cm.
(ii) Draw the right bisector of BC, cutting BC at O.
(iii) With O as centre and radius OB, draw a semicircle on BC.
(iv) With B as centre and radius 4 cm, draw an arc, cutting the semicircle at A.
(v) Join AB and AC.
Then, `Delta ABC` is the required triangle, right angled at A.
Justification :
We know that an angle in a semicircle is a right angle and therefore, `angleBAC=90^(@)`.
Also, `BA=4` cm and `BC=6` cm.
Hence, `Delta ABC` is the required triangle, right angled at A.