Question

Construct a right angled triangle PQR, in which $\angle Q={90}^o$,hypotenuse PR=8 cm and QR=4.5 cm. Draw bisector of angle PQR and let it meet PR at point T. Prove that T is equidistant from PQ and QR.

Answer 1

Steps of Construction:

i) Draw a line segment QR = 4.5 cm

ii) At Q, draw a ray QX making an angle of

iii) With centre R and radius 8 cm, draw an arc which intersects QX at P.

iv) Join RP.

is the required triangle.

v) Draw the bisector of which meets PR in T.

vi) From T, draw perpendicular PL and PM respectively on PQ and QR.

Proof: In and

Hence, T is equidistant from PQ and QR.