Similar Triangles (Flash cards)

What are similar triangles?

• Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

• Triangles that have the same size and shape, with all sides and angles equal.

• Triangles that have different shapes but the same area.

• Triangles that are always right-angled and have one angle equal to 90 degrees.

What is the relationship between the sides of similar triangles?

• The ratios of the lengths of corresponding sides of similar triangles are equal.

• The lengths of corresponding sides are always equal.

• The sum of the lengths of the sides is equal in similar triangles.

• The angles of similar triangles are always equal.

What is the first step in determining if two triangles are similar?

• Identify and compare the angles of both triangles.

• Calculate the area of both triangles.

• Measure the lengths of the sides of both triangles.

• Check if the triangles are congruent.

What is the significance of the included angle in the SAS postulate?

• The included angle must be equal for the triangles to be considered similar under the SAS postulate.

• The included angle must be greater than 90 degrees for the triangles to be similar.

• The included angle can vary as long as the sides are proportional.

• The included angle is irrelevant to the similarity of the triangles.

Provide an example of using the AA postulate to prove similarity.

• If Triangle ABC has angles of 30°, 60°, and 90°, and Triangle DEF has angles of 30°, 60°, and 90°, then Triangle ABC ~ Triangle DEF by AA.

• If Triangle GHI has angles of 45°, 45°, and 90°, and Triangle JKL has angles of 30°, 60°, and 90°, then Triangle GHI ~ Triangle JKL by AA.

• If Triangle MNO has angles of 30°, 60°, and 90°, and Triangle PQR has angles of 60°, 60°, and 60°, then Triangle MNO ~ Triangle PQR by AA.

• If Triangle STU has angles of 30°, 30°, and 120°, and Triangle VWX has angles of 30°, 60°, and 90°, then Triangle STU ~ Triangle VWX by AA.

What is the AA similarity postulate?

• If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

• If the sides of one triangle are proportional to the sides of another triangle, then the triangles are similar.

• If two sides of one triangle are equal to two sides of another triangle, then the triangles are congruent.

• If the angles of a triangle sum up to 180 degrees, then the triangle is valid.

How do you apply the SAS postulate in a problem?

• Verify that two sides of one triangle are proportional to two sides of another triangle and that the angle between those sides is equal.

• Check that all three sides of the triangles are equal in length.

• Ensure that the angles of both triangles are equal and the sides are not proportional.

• Determine that one triangle is a right triangle and the other is not.

Can two triangles be similar if only one pair of angles is equal?

• Yes, they can be similar with one pair of angles equal.

• No, at least two pairs of angles must be equal for the triangles to be similar.

• Yes, if the sides are proportional.

• No, similarity is determined by the lengths of the sides only.

What is the SAS similarity postulate?

• If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

• If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

• If the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.

• If the ratio of the lengths of two sides of one triangle is equal to the ratio of the lengths of two sides of another triangle, then the triangles are similar.

What does it mean if two triangles are not similar?

• Their corresponding angles are equal, and their corresponding sides are in proportion.

• Their corresponding angles are not equal, and their corresponding sides are not in proportion.

• Their corresponding angles are equal, but their corresponding sides are not in proportion.

• Their corresponding angles are not equal, but their corresponding sides are in proportion.