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, $AB$,
and altitudes $h$ and $k$ from $A$ and $B$ respectively.
(Using straightedge-compass construction)

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

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

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

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

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

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

The required triangle is $\Delta ABC.$

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.