Exploring Similar Triangles

What criteria must two triangles meet to be considered similar?

• Two triangles must have one equal angle and one equal side to be similar.

• Two triangles must have equal corresponding angles and proportional corresponding sides to be similar.

• Two triangles must have all sides equal to be similar.

• Two triangles must have equal areas and equal perimeters to be similar.

If triangle A has sides of length 3, 4, and 5, and triangle B has a side of length 6, what is the length of the other two sides if they are similar?

• 4.0, 5.0

• 3.6, 4.8

• 2.4, 3.2

• 5.0, 6.0

In triangle X, the sides are 8 cm, 6 cm, and 10 cm. Triangle Y has a side of 4 cm. Are triangles X and Y similar? Why or why not?

• No, triangles X and Y are not similar.

• Yes, triangles X and Y are similar because they have one side in common.

• No, triangles X and Y are similar because they have proportional sides.

• Yes, triangles X and Y are similar because they have the same angles.

If two similar triangles have a side ratio of 2:5, and one side of the smaller triangle is 10 cm, what is the corresponding side length in the larger triangle?

• 30 cm

• 25 cm

• 20 cm

• 15 cm

Triangle P has sides of 5 cm, 12 cm, and 13 cm. Triangle Q has sides of 15 cm, 36 cm, and 39 cm. Are these triangles similar? Explain your reasoning.

• Yes, the triangles are similar.

• No, the triangles are similar because they both have a right angle.

• Yes, the triangles are similar but only because they have one side in common.

• No, the triangles are not similar because they have different side lengths.