**Assignemnt #4**

**Orthocenter
of a Triangle**

**by**

**Kimberly
Burrell**

**The ****orthocenter****
of a triangle is located at the intersection of the altitudes of
the sides of the triangles.**

**It is intersecting to examine the location of the
orthocenter for different classifications of triangles.**

**ACUTE
TRIANGLES**

**Acute
Isosceles**

**In this instance, the
orthocenter is located in the interior of triangle.**

**Acute
Scalene**

**Again, the orthocenter is located in the interior of
the given triangle.**

**Acute
Equilateral**

**In this final classification of
acute triangles, we again find that the orthocenter is inside the
triangle. To explore, ****click
here****.**

**CONCLUSION: The orthocenter of
any acute triangle is located in the interior of the triangles.**

**RIGHT
TRIANGLES**

**Right
Isosceles**

**In this instance, we see that
the orthocenter is located at the vertex C, opposite the
hypotenuse of the right triangle.**

**Right
Scalene**

**Again, we find that the
orthocenter is located at the vertex C, opposite the hypotenuse
of the right triangle.**

**CONCLUSION: The orthocenter of a right triangle is
located at the vertex C, opposite the hypotenuse of the right
triangle.**

**OBTUSE
TRIANGLES**

**Obtuse
Scalene**

**In this case, we see that the
orthocenter is located outside of the given triangle. Also,
notice that it is opposite the longest side and behind the obtuse
angle.**

**Obtuse
Isosceles**

**We find the same situation in
this instance. The orthocenter is outside the triangle, opposite
the longest side, and behind the obtuse angle.**

**CONCLUSION: The orthocenter of
an obtuse triangle is located outside the triangle, opposite the
longest side, and behind the obtuse angle.**