1. ## Triangle Construction

Does anyone have an algorithm for constructing a triangle given one side, AB, and altitudes h and k from A and B respectively? (Using straightedge compass construction)

2. Hello, GoldendoodleMom!

Find an algorithm for constructing a triangle given one side, $\displaystyle AB$,
and altitudes $\displaystyle h$ and $\displaystyle k$ from $\displaystyle A$ and $\displaystyle B$ respectively.
(Using straightedge-compass construction)

Draw line segment $\displaystyle AB.$
Locate its midpoint $\displaystyle M.$
Draw a semicircle with diameter $\displaystyle AB.$
Code:
              * * *
*           *
*               *
*                 *

*                   *
A * - - - - * - - - - * B
M

With $\displaystyle A$ as center and radius $\displaystyle h$, swing an arc cutting the semicircle at $\displaystyle P.$

With $\displaystyle B$ as center and radius $\displaystyle k$, swing an arc cutting the semicircle at $\displaystyle Q.$

Code:
              Q
∆ * *     P
*     ∆     o
*         ∆     *
*       o    ∆    *
o         ∆
*  o              ∆ *
A o - - - - * - - - - ∆ B
M

Draw $\displaystyle AQ$ and $\displaystyle BP$, extending them to meet at $\displaystyle C.$

The required triangle is $\displaystyle \Delta ABC.$

3. ## Triangle Construction

Hello
For the past few days, I've been searching on the Internet for a triangle construction from its orthocenter, circumcenter and incenter. Unfortunately,I didn't find anything. Does anyone know something about this construction?
Thank you.