Congruent Shapes Through Transformation

When a shape has the the same size, shape, and measure.

• similar

• corresponding

• congruent

• equal

Translations are always _______

• Congruent

• Bigger

• Smaller

• Rotated

Determine how to translate triangle ABC to triangle A'B'C'.

• left 2, up 9

• right 2, down 9

• left 2, down 9

• left 2, up 5

Which of the following is a way to prove that triangle ABC is congruent to triangle FED?

• Rotation of 180 degrees in the middle of vertices c and d.

• Triangle ABC can be translated down two units, right 3 units and then reflected over a vertical line that goes through point d.

• A single reflection over a vertical line halfway between the two triangles.

• Triangle ABC can be translated down two units and then reflected over a horizontal line that goes through point d.

Tell whether the two figures are congruent.

• Yes, same size and same shape

• No, same shape but different sizes

• No, different size and different shapes

For each pair of shapes, decide whether or not quadrilateral ABCD is congruent to quadrilateral EFGH. Explain your reasoning.

• Yes, rotate quadrilateral ABCD 180 degrees using point d as the center, then translate 1 unit right and 2 units down.

• Yes, rotate quadrilateral ABCD 90 degrees counterclockwise using point d as the center, then translate 1 unit right and 2 units down.

• No, there are no sets of transformations that would map/overlap quadrilateral ABCD onto quadrilateral EFGH because the shapes are not congruent.

Is figure A congruent to figure B?

• Yes, figure A can be rotated 180 degrees from the origin to become figure B.

• Yes, figure A can reflected over the x-axis, then translated 4 units to the right to become figure B.

• No, figure B is too small to be a rotation of figure A.

• No, figure A cannot be transformed to become figure B.

Are the two shapes congruent?

• No, there are no sets of transformations that map/overlap the top triangle onto the bottom triangle because the shapes are not congruent.

• Yes, you can make the top triangle smaller, then reflect it over a diagonal line.

• Yes, you can reflect the top triangle over a diagonal line.

• Yes, rotate the top triangle 60 degrees clockwise, then translate it down.

Are the two figures congruent?

• Yes, you can rotate figure A 90 degrees clockwise to line up with figure B.

• No, these two figures are not congruent through transformations because the side lengths and angles are not equal.

• Yes, you can rotate figure A 180 degrees to line up with figure B.

Are these two figures congruent?

• No, the two ovals are not facing the same way.

• Yes, you can reflect the left oval 90 degrees clockwise to become the oval on the right.

• No, these two ovals are not congruent.

• Yes, you can rotate the left oval 90 degrees clockwise to become the oval on the right.