LEARNATHON

III

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

Learn more### Theory:

Let us learn how to construct a triangle with an example when its base, vertical angle and the altitude from the vertex to the base are given.

Example:

Construct a \(\triangle ABC\) such that \(AB = 5 \ cm\), \(\angle C = 45^{\circ}\), and the altitude from \(C\) to \(AB\) is of length \(2 \ cm\).

**Solution**:

First, let us draw a rough figure.

**Construction**:

**Step 1**: Draw a line segment \(AB\) of length \(5 \ cm\).

**Step 2**: At \(A\), draw \(AE\) such that \(\angle BAE = 45^{\circ}\).

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

**Step 4**: Draw the perpendicular bisector \(XY\) to \(AB\), which intersects \(AD\) at \(G\) and \(AB\) at \(F\).

**Step 5**: With \(G\) as centre and \(GA\) as radius, draw a circle \(ABH\).

**Step 6**: From \(F\), mark an arc in the line \(XY\) at \(I\), such that \(FI = 2 \ cm\).

**Step 7**: Draw \(NM\) through \(I\), which is parallel to \(AB\).

**Step 8**: \(NM\) meets the circle at \(A\) and \(J\).

**Step 9**: Join \(AB\) and \(AC\). Thus, \(ABC\) is the required triangle.