Triangles: Similarity and Congruence Concepts

What is the primary difference between congruent and similar triangles?

• Congruent triangles have different sizes and shapes, while similar triangles have the same size and shape.

• Congruent triangles have the same size but different shapes, while similar triangles have the same shape but different sizes.

• Congruent triangles have the same size and shape, while similar triangles have the same shape but not necessarily the same size.

• Congruent triangles have the same shape but different sizes, while similar triangles have the same size and shape.

Which of the following is true for congruent triangles?

• Corresponding sides have the same length.

• The triangles have different shapes.

• Corresponding angles are not equal.

• Corresponding sides are proportional.

What must be true for two triangles to be considered similar?

• They must have the same size.

• Their corresponding angles must be congruent, and their corresponding sides must be proportional.

• They must have the same perimeter.

• Their corresponding sides must be equal.

Which of the following is a valid criterion for triangle similarity?

• Side-Angle-Side (SAS)

• Angle-Angle-Angle (AAA)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

If two triangles have two pairs of congruent angles, what can be concluded?

• The triangles are neither congruent nor similar.

• The triangles have the same area.

• The triangles are similar.

• The triangles are congruent.

In a pair of similar triangles, if one side of the first triangle is 8 inches and the corresponding side of the second triangle is 4 inches, what is the ratio of their sides?

• 3:2

• 2:1

• 1:1

• 1:2

Which of the following is an example of using similar triangles in real life?

• Finding the height of a tree using its shadow.

• Calculating the area of a triangle.

• Determining the perimeter of a triangle.

• Measuring the angles of a triangle.

If a tree casts a shadow 45 feet long and a 3-foot stick casts a shadow 5 feet long, what is the height of the tree?

• 30 feet

• 27 feet

• 15 feet

• 9 feet

What is the purpose of using proportions in similar triangles?

• To find the area of the triangles.

• To determine the congruence of the triangles.

• To calculate the perimeter of the triangles.

• To solve for unknown side lengths.

In the context of similar triangles, what does the term 'proportional' refer to?

• Equal angles

• Equal perimeters

• Equal side lengths

• Equal ratios of corresponding side lengths