Lesson 10

Bases and Heights of Triangles

Lesson Narrative

This lesson furthers students’ ability to identify and work with a base and height in a triangle in two ways:

1. By learning to draw (not just to recognize) a segment to show the corresponding height for any given base, and

2. By learning to choose appropriate base-height pairs to enable area calculations.

Students have seen that the area of a triangle can be determined in multiple ways. Using the base and height measurements and the formula is a handy approach, but because there are three possible pairs of bases and heights, some care is needed in identifying the right combination of measurements. Some base-height pairs may be more practical or efficient to use than others, so it helps to be strategic in choosing a side to use as a base.

Learning Goals

Teacher Facing

• Draw and label the height that corresponds to a given base of a triangle, making sure it is perpendicular to the base and the correct length.
• Evaluate (orally) the usefulness of different base-height pairs for finding the area of a given triangle.

Student Facing

Let’s use different base-height pairs to find the area of a triangle.

Required Preparation

From the geometry toolkit, each student especially needs an index card for the Hunting for Heights activity.

Student Facing

• I can identify pairs of base and corresponding height of any triangle.
• When given information about a base of a triangle, I can identify and draw a corresponding height.

Glossary Entries

• edge

Each straight side of a polygon is called an edge.

For example, the edges of this polygon are segments $$AB$$, $$BC$$, $$CD$$, $$DE$$, and $$EA$$.

• opposite vertex

For each side of a triangle, there is one vertex that is not on that side. This is the opposite vertex.

For example, point $$A$$ is the opposite vertex to side $$BC$$.

• vertex

A vertex is a point where two or more edges meet. When we have more than one vertex, we call them vertices.

The vertices in this polygon are labeled $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$.