Exploring Similarity Theorems in Geometry

What does the AA similarity theorem state?

• Two triangles are similar if they have two pairs of proportional sides.

• Two triangles are similar if they have one pair of congruent angles.

• Two triangles are similar if they have two pairs of congruent angles.

• Two triangles are similar if they have three pairs of congruent sides.

Which of the following is an example of similar triangles according to the AA similarity theorem?

• Two triangles with angles 45°, 45°, 90° and 30°, 60°, 90°.

• Two equilateral triangles with angles 60°, 60°, 60°.

• Two triangles with sides 3, 4, 5 and 6, 8, 10.

• Two triangles with sides 5, 12, 13 and 10, 24, 26.

What is required to prove two triangles are similar using the SSS similarity theorem?

• Two pairs of proportional sides and one pair of congruent angles.

• Three pairs of proportional sides.

• One pair of congruent sides and one pair of congruent angles.

• Two pairs of congruent angles.

In the SAS similarity theorem, what must be true about the included angle?

• It must be complementary.

• It must be supplementary.

• It must be proportional.

• It must be congruent.

If two triangles have sides in the ratio 3:4:5 and 6:8:10, are they similar?

• Yes, by the SSS similarity theorem.

• No, they are not similar.

• Yes, by the AA similarity theorem.

• Yes, by the SAS similarity theorem.

How can you solve for an unknown side in similar triangles?

• By setting up a proportion between corresponding sides.

• By using the Pythagorean theorem.

• By using the area formula.

• By using the perimeter formula.

What is the value of x if the sides of two similar triangles are in the ratio 3:5 and the corresponding sides are 3 and x?

• 7.5

• 6

• 10

• 5

Which sides should be compared to check for proportionality in similar triangles?

• The smallest side of one triangle with the smallest side of the other.

• Any side of one triangle with any side of the other.

• The smallest side of one triangle with the largest side of the other.

• The largest side of one triangle with the smallest side of the other.

In a geometric proof, what is the first step to prove two triangles are similar?

• Identify the given information.

• Set up a proportion.

• Find the perimeter.

• Calculate the area.

What is the final step in proving two triangles are similar using the AA similarity theorem?

• Show that the sides are proportional.

• Show that the triangles have the same area.

• Show that the triangles are congruent.

• Show that the angles are congruent.