Unit 1, Lesson 13
Congruence
Grade 8
13.1
Warm-up
13.2
Activity
Are any of the ovals congruent to one another? Explain how you know.
13.3
Activity
Here are two congruent shapes with some corresponding points labeled:
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On the bottom figure, draw the points corresponding to , , and , and label them , , and .
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Draw line segments and and measure them. Do the same for segments and and for segments and . What do you notice?
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Do you think there could be a pair of corresponding segments with different lengths? Explain.
13.4
Activity
Are these faces congruent? Explain your reasoning.
Student Lesson Summary
To show two figures are congruent, one is aligned with the other by a sequence of rigid transformations. This is true even for figures with curved sides. Distances between corresponding points on congruent figures are always equal, even for curved shapes.
For example, corresponding segments and on these congruent ovals have the same length:
Two congruent ovals on a square grid. In the first oval, two points on opposite longer sides of the oval are labeled A and B and are connected by a line segment. In the second oval, two points on opposite longer sides of the oval are labeled A prime and B prime and are connected by a line segment. Let the lower left corner be (0 comma 0). Then point A is near (5 comma 4 point 75) and point B is near (1 comma 3 point 7 5). Point A prime is near (9 comma 5) and point B prime is near (10 point 5 comma 1 point 3).
To show two figures are not congruent, you can find parts of the figures that should correspond but that have different measurements.
For example, these two ovals don’t look congruent.
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 shows they are not congruent.
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