Congruent and Similar Figures on Coordinate Plane

Congruence

• when a shape is enlarged

• when two figures are the same size and same shape

• when the rotation moves two quadrants

Similarity

• when shapes have the same side lengths

• when two figures are the same shape and have proportional sides and congruent angles, but not always the same size

• when we plot on coordinate plane

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75

• 9.75

• 10

• 12

Two objects that are the same shape but not the same size are _______.

• Congruent

• Vertical

• Similar

• Complementary 

When talking about figures on a coordinate plane, what does "similar" mean?

• Same shape, side lengths are proportional and angle measure are the same

• Same shape, side length are different and angles are different

• Different shape, different sizes

• Shapes sort of the same, but sides and angles are different

When talking about figures on a coordinate plane, what does "congruent" mean?

• Same shape, same size

• Same shape, size changes

• Different shape, different size

• Same shape, different size

Which transformation(s) create(s) congruent figures?

• Dilation

• Translation, Reflection, Rotation

• Dilation and Translation

• Dilation and Reflection

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

Are these triangles similar?

• Yes

• No

A pentagon graphed on a coordinate plane underwent a rotation about the origin, a reflection across the y–axis, a translation down, and a dilation with a scale factor of 3 from its center to produce another pentagon. Which of these statements is true about the original pentagon and the new pentagon?

• They are similar.

• They may or may not be similar, depending on the number of units translated.

• They may or may not be similar, depending on the number of degrees rotated.

• They are not similar.