0.3.8 What is the Same?
Lesson Objectives
Experiment with two-dimensional shapes and
decide what it means for them to be congruent.
Required Materials
geometry toolkits
Formalize definition of congruence.
Setup: Find the Right Hands (5 minutes)
Statement
A person’s hands are mirror images of each other. In
the diagram, the left hand is labeled. Shade all of the
right hands.
Anticipated Responses
Setup: Are They the Same? (15 minutes)
Access to geometry toolkit. 5 minutes quiet work time, 4 minutes sharing, followed by 6 minute class discussion.
Statement
Anticipated Responses
For each pair of shapes, decide whether or not they
are the same.
1. Same
2. Not the same
3. Same
4. Not the same
5. Same
Setup: Area, Perimeter, and Congruence (10 minutes)
4--5 minutes quiet work time, access to geometry toolkit.
Statement
Anticipated Responses
The 1 unit by 6 unit rectangles have the same area as
the blue rectangle but different perimeter. The 1 unit
by 4 unit rectangles have the same perimeter but
different area than the blue rectangle. The 2 unit by 3
unit rectangles have the same area and the same
perimeter as the blue rectangle. The congruent
rectangles have the same dimensions.
1. Which of these rectangles have the same area as
rectangle
but a different perimeter?
2. Which rectangles have the same perimeter but
different areas?
3. Which have the same area and the same
perimeter?
4. Use materials from the geometry tool kit to decide
which rectangles are congruent. Shade congruent
rectangles with the same color.
Setup: Mirror Images (5 minutes)
Cool-down (5 minutes)
Anticipated Responses
Figure B is the image of Figure A when reflected
Yes, they are congruent.
across line . Are Figure A and Figure B congruent?
Explain?
Lesson Summary (5 minutes)
How do we know if two shapes are congruent? What are some properties that are shared by congruent shapes?