Lesson 10: Bases and Heights of Triangles
About this lesson
This lesson furthers students’ ability to identify and work with a base and height in a triangle in two ways:
 By learning to draw (not just to recognize) a segment to show the corresponding height for any given base, and
 By learning to choose appropriate baseheight 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 baseheight 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 Warmup: 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 Cooldown: 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 baseheight pairs for finding the area of a given triangle.
Learning goals (student facing):
 Let’s use different baseheight 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 20172019 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/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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