 Lesson plan

# Lesson 10: Bases and Heights of Triangles

teaches Arizona State Standards 6.G.A.1
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards 6.EE.A.2.c http://corestandards.org/Math/Content/6/EE/A/2/c
teaches Common Core State Standards 6.G.A.1 http://corestandards.org/Math/Content/6/G/A/1
teaches Georgia State Standards MGSE6.G.1.
teaches Kansas State Standards 6.G.1.
teaches New York State Standards NY-6.G.1.
teaches New York State Standards NY-6.EE.2c.
teaches Ohio State Standards 6.G.1.
teaches Pennsylvania State Standards CC.2.3.6.A.1.

# Lesson 10: Bases and Heights of Triangles

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.

Lesson overview

• 10.1 Warm-up: An Area of 12 (10 minutes)
• There is a digital applet in this activity.
• 10.2 Activity: Hunting for Heights (25 minutes)
• 10.3 Optional Activity: Some Bases Are Better Than Others (15 minutes)
• Includes "Are you Ready for More?" extension problem
• Lesson Synthesis
• 10.4 Cool-down: Stretched Sideways (5 minutes)

Learning goals:

• 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.

Learning goals (student facing):

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

Learning targets (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.

Required materials:

• geometry toolkits

Required preparation:

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

Glossary:

• 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 $$EA$$. • 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 $$E$$. • Access the complete Grade 6 glossary.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.