Math CentralQuandaries & Queries


Question from Eileen, a student:

Use a formal Statement/Reason Proof to prove the following.  Include a diagram, labeled appropriately.

Given:  Acute triangle ABC, with a, b, c, being the respective opposite sides to angle A, angle B, angle C, and altitude, h, drawn from angle B to b.

Prove:  The area of triangle ABC=1/2abSin C

How would I do this??

Hi Eileen.

There are many ways to do it. I would start by drawing the triangle, inside the rectangle (remember that the altitude h is perpendicular to the base b).

First, you can say that the area of the rectangle is hb. Then you can reason that the triangle's area is ½hb since it neatly divides the rectangle into two pairs of congruent triangles.

Now look at the right triangle I've shaded. Can you find an expression for h in terms of a and C? If so, replace h in the ½hb calculation and you will have proved the solution.

Stephen La Rocque.

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