Triangle Similarity and Dilation Concepts

This lesson, led by Mrs. Apia, explores the concept of similar triangles, focusing on the angle-angle criterion and the use of scale factors to determine similarity. Through various examples, the lesson demonstrates how to prove triangle similarity by analyzing corresponding angles and sides, using dilation and parallel lines. The lesson concludes with a summary of key concepts and methods for finding missing measurements in similar triangles.

What is the angle-angle criterion for triangle similarity?

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

• Two triangles are similar if they have proportional sides.

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

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

What is required to use the angle-angle criterion to prove triangle similarity?

• Proportional sides.

• Three pairs of corresponding congruent angles.

• Two pairs of corresponding congruent angles.

• One pair of corresponding congruent angles.

In Example 1, what method is used to establish the similarity between triangles ABC and DEF?

• Using the hypotenuse-leg criterion.

• Using the side-side-side criterion.

• Using dilation and parallel lines to establish congruent angles.

• Using the angle-side-angle criterion.

What is the role of dilation in proving triangle similarity?

• Dilation ensures the triangles have equal areas.

• Dilation changes the shape of the triangle.

• Dilation helps establish congruent angles and proportional sides.

• Dilation makes the triangles congruent.

Why are triangles ABC and ABC Prime not similar in Example 2?

• The triangles have different shapes.

• The ratios of the adjoining sides are not equal.

• The triangles have different areas.

• The triangles have no congruent angles.

In Example 3, how is the length of side AB Prime determined?

• By using the angle-side-angle criterion.

• By using the side-side-side criterion.

• By using the scale factor derived from the similarity statement.

• By using the hypotenuse-leg criterion.

What is the significance of parallel lines in determining triangle similarity in Example 4?

• Parallel lines ensure the triangles have equal areas.

• Parallel lines ensure the triangles have equal side lengths.

• Parallel lines ensure the triangles have equal perimeters.

• Parallel lines ensure the corresponding angles are congruent.

In Example 5, why can't the similarity of triangles OPQ and OP'Q' be determined?

• The triangles have no congruent angles.

• The triangles have different shapes.

• The necessary side lengths for calculating the scale factor are missing.

• The triangles have different areas.

How can missing measurements be found in similar triangles?

• By using the hypotenuse-leg criterion.

• By using the side-side-side criterion.

• By using the angle-side-angle criterion.

• By using the ratio of the corresponding sides.

What does it mean if two triangles have the same scale factor for their sides?

• The triangles have equal perimeters.

• The triangles have equal areas.

• The triangles are similar.

• The triangles are congruent.