UPSKILL MATH PLUS
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Learn moreLearn 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.
![11 Ресурс 2.png](https://resources.cdn.yaclass.in/1eaeed27-26ee-4a81-a5bf-505b015beba0/11%D0%A0%D0%B5%D1%81%D1%83%D1%80%D1%812w300.png)
Construction:
![11 Ресурс 1.png](https://resources.cdn.yaclass.in/58b90ba4-fc6d-4985-9de4-06de9c3e19c8/11%D0%A0%D0%B5%D1%81%D1%83%D1%80%D1%811w400.png)
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: Draw a circle with \(O\) as the centre and \(OA\) as the radius.
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.