Question

Construct a triangle ABC, whose perimeter is 12.5 cm and whose base angles are 50° and 80° .

Answer 1

see ur NCERT Book .............. if u do not understand then I will tell u

Answer 2

Construction steps :

1 ) Draw rough skatch of a triangle ABC

and mark the given measures.

2 ) Draw a line segment XY = 12.5 cm

( As AB+BC + CA = 12.5 Perimeter )

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

and AY .

5 ) Draw perpendicular bisectors of

AX and AY to intersect XY ray at B

and C respectively.

Join AB and AC .

Then , ABC is the required triangle .

___________________________

Justify the construction as follows :

Proof :

B lies on the perpendicular bisector

PQ of AX .

Therefore ,

XB = AB and

similarly CY = AC

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

= XY

Again <BAX = <AXB

[ Since, XB = AB in ∆AXB ] and

<ABC = <BAX + <AXB

[ Exterior angle of ∆ABC ]

= 2<AXB

= <YXL

= 50°

Similarly<ACB = <XYM = 80°

as required

Therefore ,

<B = 50° and <C = 80°

as given are constructed.

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