What Is the Same?

Warmup

A person’s hands are mirror images of each other. In the diagram, a left hand is labeled. Mark all of the right hands.

Activity #1

Identify Congruent Figures.

• Compare the shapes in the applet below and answer the questions that follow..

(1.) Which of these rectangles have the same area as Rectangle R but different perimeter?

(2.) Which rectangles have the same perimeter as Rectangle R but different area?

(3.) Which have the same area and the same perimeter as Rectangle R?

(4.) Use materials from the geometry tool kit to decide which rectangles are congruent. (Mark congruent rectangles with the same color.)

In square ABCD, points E, F, G, H are midpoints of their respective sides.

(1.) What fraction of square ABCD is shaded?

(2.) Explain your reasoning.

Activity #2

Determine Whether Two Shapes are Congruent or not Congruent.

• Draw two rectangles that have the same area, but are not congruent.

(1.) Decide whether or not the two shapes below are congruent. Explain your reasoning.

(2.) Decide whether or not the two shapes below are congruent. Explain your reasoning.

Activity #3

Explore More on Congruent Shapes.

• Reflect Quadrilateral A over the x- axis.
• Label the image quadrilateral as B.
• Reflect Quadrilateral B over the y-axis.
• Label the image as C.

(1.) Are Quadrilaterals A and C congruent?

(2.) Explain how you know.

Challenge #1

(1.) If two rectangles have the same perimeter, do they have to be congruent? Use the applet below to explain how you know.

(2.) If two rectangles have the same area, do they have to be congruent? Use the applet below to explain how you know.

Challenge #2

The point (-2, -3)  is rotated 90 degrees counterclockwise using center (0, 0).

Challenge #3

The point (-2, -3) is rotated 90 degrees counterclockwise using center (0, 0).