Question

Construct a triangle ABC whose perimeter 12 cm and whose base angles are 50° and 80°

Answer 1

please refer NCERT Book

Answer 2

Steps of construction :

1 ) Draw a rough skatch of a triangle

ABC and mark the given measures.

2 ) Draw a line segment XY = 12cm

[ As XY = AB + BC + CA ]

3 ) Construct <YXL = 50° and <XYM = 80°

and draw bisectors of these angles.

4 ) Let the bisectors of these angles

intersect at a point A and join AX or AY.

5 ) Draw perpendicular bisectors of AX

and AY to intersect XY at B and C

respectively .

Join AB and AC .

Then , ABC is the required triangle.

Proof :

B lies on the perpendicular bisector

PQ of AX .

XB = AB and similarly CY = AC

This gives AB + BC + CA = XB+BC+CY

= XY

Again <BAX = <AXB

[ XB = AB in ∆AXB ] and

= 2<AXB

= <YXL

= 50°

Similarly <ACB = <XYM = 80° as

required <B = 50° and <C = 80°

as given are constructed.

•••••