**Assignment #8**
**Nicole Mosteller**
**EMAT 6680**

**Altitudes and Orthocenters**
The first interesting property in this investigation of altitudes and orthocenters occurs when finding the orthocenter
of the triangle whose vertices are two vertices of the original triangle and the orthocenter of the original triangle.
__Figure 1:__ **H** is the orthocenter of the original **DABC**.
The orthocenter for **DACH** has label **H1** and is point **B**.
Once we recall how point **H** is located, it will be clear why **H1** and **B** are the same points.
**H** is on the line (**BH**) containing **B** that is perpendicular to segment **AC**,
**H** is on the line (**AH**) containing **A** that is perpendicular to segment **BC**, and
**H** is on the line (**CH**) containing **C** that is perpendicular to segment **AB**.
To find the orthocenter of **DACH**, notice that the perpendiculars to the sides **AH** and **CH**
are sides of **DABC **(sides **AB** and **CB**). These segments clearly intersect at point B.
Recall that the line perpendicular to side **AC** through **H** contains point **B**.
**B is the orthocenter of DACH.**

**Why are the circumcircles of the original DABC, DABH, DBCH, and DACH congruent? **

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