# I have Another Triangle Question!!!!!

• October 14th 2008, 02:02 PM
joesmith13610
I have Another Triangle Question!!!!!
Construct triangle given side a, Ha(height at side A), Ma(median of side a).

for this problem is it possible that Ha = Ma? Cause this is where I am stuck.
if Ha = Ma, then my problem is solved, because they both meet at the perpendicular bisector of side a, which is where the midpoint lie. Which means my median and height will also intersect. right??

• October 14th 2008, 03:26 PM
Soroban
Hello, Joe!

The wording is rather clumsy . . .

Quote:

Construct a triangle given: side $a,\;H_a$ (altitude to side $a$), $M_a$ (median to side $a$).

Draw a horizontal line $L.$

Erect a perpendicular to line $L$ and measure length $H_a$ to point $A.$
Code:

```          A           *           |           |       Ha |           |           |     L - - * - - - - - - - - - - - - - -```

Using center $A$ and radius $M_a$, swing an arc cutting line $L$ at $D.$
Code:

```          A           *           |\           | \       Ha |  \ Ma           |  \           |    \     L - - * - - * - -                 D```

$D$ is the midpoint of side $a.$

Using center $D$ and radius $\tfrac{1}{2}a$, swing arcs on both sides
. . cutting line $L$ at $B$ and $C.$
Code:

```          A           *         *|\ *         * | \  *       *  |  \    *       *  |  \      *     *    |    \        *     *  *  *  *  *  *  *  *  *     B    ½a    D    ½a    C```

And $ABC$ is our triangle!

• October 14th 2008, 03:54 PM
joesmith13610
so we first construct a line segment BD that is 1/2 of length side a, and find the perpendicular bisector? is that correct?