Question

Use ruler and compasses only for this question.
Construct a triangle ABP such
that AB = 5 cm, BP = 4 cm and angle ABP = 30°. Complete the rhombus ABCD such
that P is equidistant from AB and BC. Locate the point Q on the line BP such
that Q is equidistant from A and B.

( Please answer the question correctly and I will mark you as a brainliest )​

Answer 1

Given:

AB = 5 cm, BP = 4 cm and angle ABP = 30°.

To construct:

A triangle ABP and a rhombus ABCD.

Steps of construction:

Draw a line AB with a scale of 5 cm

From point B, with an angle of 30° and a scale of 4 cm draw a line segment.

Mark the other point as P.

Join AP.

Hence the required construction of ∆ ABP.

Since P is equidistant from AB and BC, P lies on  the bisector of ∠ ABC.

Given, ∠ ABP = 30°, therefore,  construct ∠ ABR = 60°.  (as 30° + 60° = 90°)

Cut off BC = 5 cm from  BR.

Join the points A, B, C and D.

Hence the required construction of rhombus ABCD.

Since Q is equidistant from A and B, draw perpendicular bisector of AB. The point  of intersection of the right bisector of AB and the line BP is the required point Q.