Lesson 4: Medians and Altitudes

DO NOW

If you are given two points, how do you find the equation of the line that passes through those two points? Try it with these two points: (-2, 0) and (3, 4)

DO NOW

What is the circumcenter of a triangle? What is the incenter? How are they the same? How are they different? Which one would you most like to take on a date?

LEARNING TARGET

I can identify properties of medians and altitudes of a triangle.

I DO

What is new today?

We are learning about two other types of special segments in a triangle. We have already learned about angle bisectors and perpendicular bisectors. Today, we are learning about medians and altitudes.

A median is a segment that connects the midpoint of a side to the opposite vertex.

An altitude is a segment that connects a vertex to the opposite side at a right angle.

Here are the relevant theorems:

Let's do some examples:

In triangle PQS, is PR a median, an altitude, or neither?
What about QT?

Let's do some harder examples:

We are moving toward more coordinate Geometry!

To solve these problems:

You need to find the equations of two altitudes (choose the easiest two lines, but any will work).

You can find the equation by finding the slope (using the slope formula), then finding the perpendicular slope (opposite reciprocal), then finding the line that has that slope and passes through the opposite vertex (point-slope form).

Horizontal and vertical sides will be easier to use.

WE DO

In triangle ABC, is each segment below a median, an altitude, or neither? Explain.

AD?

CF?

EG?

YOU DO

Complete these problems and these problems (front for a 3, and back for a 4). Here is a document that explains how to do this.

Extra practice (try to find the orthocenter using a compass and straight edge) (one point for each page)

INdependent review

Video and explanation about finding the orthocenter

Below, review all the special centers together:

Page updated

Report abuse