Understanding Triangle Similarity

What is the definition of similar triangles?

• Triangles that have equal corresponding angles and proportional corresponding sides.

• Triangles that are all right-angled and have equal areas.

• Triangles that have unequal corresponding angles and proportional sides.

• Triangles that have equal sides and different angles.

How can you determine if two triangles are similar?

• Triangles are similar if they are both right triangles.

• Triangles are similar if corresponding angles are equal and sides are in proportion.

• Triangles are similar if they have the same area.

• Triangles are similar if they have one equal side.

What is the Angle-Angle (AA) similarity criterion?

• If two triangles have two equal angles, they are similar.

• If two triangles have three equal sides, they are similar.

• If two triangles have one equal angle, they are similar.

• If two triangles have equal perimeters, they are similar.

Explain the Side-Side-Side (SSS) similarity criterion.

• If one triangle is larger than another, they are similar.

• If the angles of two triangles are equal, they are similar.

• If two triangles have the same area, they are similar.

• If the corresponding sides of two triangles are in proportion, the triangles are similar.

What is the Side-Angle-Side (SAS) similarity criterion?

• If two triangles have two pairs of sides in proportion, they are similar.

• If two triangles have all three sides in proportion, they are similar.

• If two triangles have equal angles, they are similar regardless of side lengths.

• If two triangles have one pair of sides in proportion and the included angle is equal, they are similar.

If two triangles have one angle equal and the sides around that angle are in proportion, what can be said about the triangles?

• The triangles are similar.

• The triangles are congruent.

• The triangles have different angles.

• The triangles are identical.

Can two triangles be similar if their corresponding sides are not in proportion? Why or why not?

• No, but they can still be congruent.

• Yes, if one triangle is a scaled version of the other.

• Yes, if they have the same angles.

• No, two triangles cannot be similar if their corresponding sides are not in proportion.

What role does the concept of scale factor play in triangle similarity?

• The scale factor changes the area of the triangles but not the sides.

• The scale factor is irrelevant in determining triangle similarity.

• The scale factor determines the proportional relationship between the sides of similar triangles.

• The scale factor only applies to the angles of similar triangles.