Math: Similar and Congruent Figures

Triangle A has side lengths 3 cm, 4 cm, and 5 cm. Triangle B has side lengths 6 cm, 8 cm, and 10 cm. Are the triangles similar, congruent, or neither? Explain.

A square has side length 7 cm. Another square has side length 7 cm. Are the squares similar, congruent, or both? Explain.

Rectangle P is 3 units wide and 8 units long. Rectangle Q is 6 units wide and 16 units long. Are the rectangles similar, congruent, or neither?

Rectangle M is 4 units by 9 units. Rectangle N is 8 units by 15 units. Are the rectangles similar, congruent, or neither? Explain.

Two triangles are congruent. One triangle has side lengths 5 cm, 12 cm, and 13 cm. What are the side lengths of the other triangle?

A photo that is 4 inches wide and 6 inches tall is enlarged so that the new width is 10 inches. What is the scale factor? What is the new height?

Figure X and Figure Y are similar. A side in Figure X is 9 cm, and the matching side in Figure Y is 12 cm. What is the scale factor from Figure X to Figure Y?

A triangle is enlarged by a scale factor of 3. If one side of the original triangle is 7 units, what is the length of the matching side in the enlarged triangle?

A rectangle is reduced by a scale factor of 1/2. If the original length is 18 cm and the original width is 10 cm, what are the new dimensions?

Explain the difference between similar figures and congruent figures.

Two pentagons have equal corresponding angles, and each side length in the larger pentagon is 3 times the matching side length in the smaller pentagon. Are the pentagons similar, congruent, or neither?

Shape A has side lengths 2 cm, 2 cm, 3 cm, and 3 cm. Shape B has side lengths 4 cm, 4 cm, 6 cm, and 6 cm. If the corresponding angles are equal, are the shapes similar, congruent, or both?

A map uses a scale where 1 inch represents 5 miles. If two towns are 3.5 inches apart on the map, how far apart are they in real life?

A model car is built at a scale of 1:20. If the real car is 180 inches long, how long is the model car?

Two figures have the same shape, but one figure is twice as large as the other. Can the figures be congruent? Can they be similar? Explain.