Lesson 11

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Congruence

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit i

Rigid Transformations

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Warm Up - Translated Images

All of these triangles are congruent. Sometimes we can take one figure to another with a translation. Shade the triangles that are images of triangle ABC under a translation.

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• I can comprehend that figures with the same area and perimeter may or may not be congruent.
• I can critique arguments (orally) that two figures with congruent corresponding sides may be non-congruent figures.
• I can justify (orally and in writing) that two polygons on a grid are congruent using the definition of congruence in terms of transformations.

Learning Targets

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Congruent Pairs

For each of the following pairs of shapes, decide whether or not they are congruent. Explain your reasoning.

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Congruent Pairs Pt.2

For each pair of shapes, decide whether or not Shape A is congruent to Shape B. Explain how you know.

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Congruent Pairs Pt.2

Ready for more??? A polygon has 8 sides: five of length 1, two of length 2, and one of length 3. All sides lie on grid lines. (It may be helpful to use graph paper when working on this problem.) 1. Find a polygon with these properties. 2. Is there a second polygon, not congruent to your first, with these properties?

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11.3 corresponding points in Congruent figures

Here are two congruent shapes with some corresponding points labeled.

1. Draw the points corresponding to B,D, and E and label them B’, D’, and E’.
2. Draw line segments AD and A’ D’ and measure them. Do the same for segments BC and B’ C’ and for segments AE and A’ E’ . What do you notice?
3. Do you think there could be a pair of corresponding segments with different lengths? Explain.

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Building Quadrilaterals

Your teacher will give you a set of four objects.

1. Make a quadrilateral with your four objects and record what you have made.
2. Compare your quadrilateral with your partner’s. Are they congruent? Explain how you know.
3. Repeat steps 1 and 2, forming different quadrilaterals. If your first quadrilaterals were not congruent, can you build a pair that is? If your first quadrilaterals were congruent, can you build a pair that is not? Explain.

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Lesson Summary

To show two figures are congruent, you align one with the other by a sequence of rigid transformations. This is even true for figures with curved sides. Distances between corresponding points on congruent figures are always equal even for curved shapes.

Corresponding segments AB and A’ B’ on these congruent ovals have the same length.

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Lesson Summary

On both, the longest distance is 5 units across, and the longest distance from top to bottom is 4 units. The line segment from the highest to lowest point is in the middle of the left oval, but in the right oval, it’s 2 units from the right end and 3 units from the left end. This proves they are not congruent.

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Lesson Summary

The main points to highlight at the conclusion of the lesson are:

• Two figures are congruent when there is a sequence of translations, rotations, and reflections that match one figure up perfectly with the other.
• When showing that two figures are congruent on a grid, we use the structure of the grid to describe each rigid motion. For example, translations can be described by indicating how many grid units to move left or right and how many grid units to move up or down. Reflections can be described by indicating the line of reflection (an axis or a particular grid line are readily available).
• Two figures are not congruent if they have different side lengths, different angles, or different areas.
• Even if two figures have the same side lengths, they may not be congruent. With four sides of the same length, for example, we can make many different rhombuses that are not congruent to one another because the angles are different.

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Cool Down: Scaling L

Are Figures A and B congruent? Explain your reasoning.

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Reflections

• Can you comprehend that figures with the same area and perimeter may or may not be congruent?
• Can you critique arguments (orally) that two figures with congruent corresponding sides may be non-congruent figures?
• Can you justify (orally and in writing) that two polygons on a grid are congruent using the definition of congruence in terms of transformations?

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Practice Problems

Must do: All problems

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ALL PERIODS click here to submit homework.

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Lesson Video

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