Making Parallelograms from Triangles

Katie AtchleyRita Byrom

Melissa Feldmann

Investigation 6.3AL COS:

4.c. Classifying triangles as right, obtuse, or acute;

5 Plot coordinates on grids, graphs, and maps.;

7 Developing formulas to determine perimeter and area of parallelograms and rectangles

Problem of the Day

   Estimate the area of the triangle with the following points:

(-4, 1), (-1, -4), (-1, 3)

Keeping two points of the original triangle the same and plotting a third point, how many parallelograms can you form?

Find the area of each parallelogram.

• We have discovered that triangles and other polygons are useful for building because they are stable figures.

• In order to maintain their stability, architects use various formulas in their designs.

Explore• Cut a triangle from your folded index card. This

should create two identical triangles.

• Trace the triangle on grid paper.

• Record: Base, height, area, perimeter.

• Experiment with putting the two triangles together to make new polygons.

• Describe and sketch the polygons that are possible.

Explore

• Can you make a parallelogram by putting together the two identical triangles?

• Record the parallelogram:

• Base, height, area, perimeter

• How does it compare to the measures of the original triangle?

Summary

• Were you always able to make a parallelogram from 2 identical triangles?

• So what do the triangle and the parallelogram have in common?

• From the activity we just did and what you already know about finding areas of parallelograms and rectangles, how can we find the area of a triangle without counting and estimating?

ReflectionIn your journal:

•In the problem of the day, explain why the areas of the parallelograms you made are the same.

•Summarize what you have discovered about finding the area of a triangle as it relates to a parallelogram.

Homework

6.3 ACE PROBLEMS

Page 60 #1 and #2

page 62 #11

page 64 #18

page 66 #22