Lesson 10

What Is the Same?

Let’s decide whether shapes are the same.

Problem 1

If two rectangles have the same perimeter, do they have to be congruent? Explain how you know.

Problem 2

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

Problem 3

For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.

  1.  
    Two oval figures. The oval on the left has the long length vertical and the right side oval has the long length horizontal. The two figures appear identical.
  2.  
    Two figures A B C D E F G and H N M L K J I. Figure H N M L K J I appears to be an image of A B C D E F G after a reflection over a vertical line and a translation.

Problem 4

  1. Reflect Quadrilateral A over the \(x\)-axis. Label the image quadrilateral B. Reflect Quadrilateral B over the \(y\)-axis. Label the image C.

    Quadrilateral A on blank coordinate plane. Quadrilateral A is in quadrant 2.

  2. Are Quadrilaterals A and C congruent? Explain how you know.

Problem 5

The point \((\text-2,\text-3)\) is rotated 90 degrees counterclockwise using center \((0,0)\). What are the coordinates of the image?

A:

\((\text-3,\text-2)\)

B:

\((\text-3,2)\)

C:

\((3,\text-2)\)

D:

\((3,2)\)

(From Unit 1, Lesson 5.)

Problem 6

Describe a rigid transformation that takes Polygon A to Polygon B.

Polygon A and its image polygon B on a coordinate plane, origin \(O\).
(From Unit 1, Lesson 6.)