Mathematics
Use ruler and compass only to construct a triangle ABP such that AB = 8 cm, BP = 5 cm and angle ABP = 30°.
(i) Complete the rhombus ABCD such that P is equidistant from AB and BC.
(ii) Locate a point Q on line BP such that Q is equidistant from A and B.
Answer
Steps of construction :
Draw a line segment AB = 8 cm.
Draw BZ such that ∠ABZ = 30°.
From BZ cut off BP = 5 cm.
Join AP.
Since, P is equidistant from AB and BC, thus it will lie on the angle bisector of angle between AB and BC.
Since, ∠ABP = 30°
∴ ∠ABR = 60°Draw ∠ABR = 60°.
From BR cut off BC = 8 cm.
With C and A as center draw arcs of 8 cm cutting each other at point D.
Join CD and AD.
Draw XY, the perpendicular bisector of AB.
Mark point Q as the intersection point of BP and XY.
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