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How to draw altitudes on bases PQ and PR from opposite vertices R and Q in a triangle PQR?
How to draw altitudes on bases PQ and PR from opposite vertices R and Q in a triangle PQR?
Solution:
An altitude in a triangle is a line segment drawn from a vertex that is perpendicular to the opposite side in the triangle. Mostly altitudes of a triangle lie within the triangle except when an obtuse angle is involved. In such cases, the altitude lies outside the triangle,
Given triangle PQR and its bases/sides PQ and PR.
To draw altitudes to PQ and PR from R and Q respectively
Steps of construction:
1. We first draw altitude to PQ from vertex R.
With R as the centre, we draw an arc of suitable radius to cut PQ in two points say A and B. With A as centre we draw another arc with the same radius. Similarly, with B as a centre, we draw another arc cutting the arc drawn above in a point C. We join RC. RC cuts PQ at right angles as a point say X. RX is the altitude to PQ.
2. Similarly, an altitude QY be drawn to the base PR of triangle PQR
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