Question

Construct ΔPQR in which QR=5.5 cm, QP=5.5 cm and ∠Q=60°. Measure RP. What kind of triangle is this?

Answer 1

The given triangle is equilateral triangle.

Because

In a triangle, " the angles opposite to equal sides are equal "

Hence
Angle P = 60 degrees
Angle R = 60 degrees

Also , angle Q = 60 degrees

The three angles are equal.

So the triangle PQR is equilateral triangle.

Answer 2

It is given that ,

In ∆PQR ,

QR = 5.5 cm

QP = 5.5 cm

<Q = 60°

Construction steps :

1 ) Draw QR = 5.5 cm line segment.

2 ) Draw <RQX = 60° at Q .

3 ) Take Q as a center and 5.5 cm radius

draw an arc which intersects QX at P.

Join PR .

∆PQR formed .

In ∆PQR ,

QR = QP = 5.5 cm

Therefore ,

<P = <R [ Angles opposite to equal sides

are equal ] -- ( 1 )

we know that ,

in ∆ PQR ,

<P + <Q + <R = 180°

<P + 60° + <P = 180°

2<P = 180° - 60°

<P = 120°/2

<P = 60°

Therefore ,

<P = <Q = <R = 60°

So , conclude that

Given triangle is an Equilateral triangle.

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