LEARNATHON

III

Competition for grade 6 to 10 students! Learn, solve tests and earn prizes!

Learn more### Theory:

Learn how to construct a triangle with an example if its base, vertical angle and the point on the base where the bisector of the vertical angle meets the base are given.

Example:

Draw a triangle \(ABC\) of base \(AB = 7 \ cm\), \(\angle C = 30^{\circ}\) and the bisector of \(\angle C\) meets \(AB\) at \(C\) such that \(AD = 5 \ cm\).

**Solution**:

First, let us draw a rough figure.

**Construction**:

**Step 1**: Draw a line segment \(AB = 7 \ cm\).

**Step 2**: At \(A\), draw \(AE\) such that \(\angle EAB = 30^{\circ}\).

**Step 3**: At \(A\), draw \(AF\) such that \(\angle FAE = 90^{\circ}\).

**Step 4**: Draw the perpendicular bisector to \(AB\), which intersects \(AF\) at \(O\) and \(AB\) at \(P\).

**Step 5**: With \(O\) as centre and \(OA\) as radius, draw a circle.

**Step 6**: From \(A\), mark an arc of \(5 \ cm\) on \(AB\) at \(D\).

**Step 7**: The perpendicular bisector intersects the circle at \(R\). Join \(RD\).

**Step 8**: \(RD\) produced meets the circle at \(C\). Now, join \(AC\) and \(AB\).

Thus, \(\triangle ABC\) is the required triangle.