Proving Triangle Similarity: SSS and SAS Methods

The video tutorial covers the concept of similar figures, focusing on triangles. It explains the properties of similar figures, such as proportional sides and equal angles. The tutorial introduces two rules for determining triangle similarity: side-side-side (SSS) and side-angle-side (SAS). The SSS rule states that two triangles are similar if their corresponding sides are proportional. The SAS rule requires two pairs of proportional sides and an included equal angle. The video includes examples to practice identifying similar triangles using these rules.

What is a key characteristic of similar figures?

• They have equal perimeters.

• They have the same area.

• They have the same volume.

• They have proportional sides and equal angles.

How many pairs of proportional sides are needed to prove two triangles are similar using the SSS criterion?

• Three pairs

• Two pairs

• Four pairs

• One pair

In the SSS similarity criterion, what must be true about the three pairs of sides?

• They must form right angles.

• They must be proportional to each other.

• They must be equal in length.

• They must be parallel.

What does the SAS similarity criterion require besides two pairs of proportional sides?

• Two pairs of equal sides.

• Two pairs of equal angles.

• An included side that is equal.

• An included angle that is equal.

In the SAS similarity criterion, what is meant by the 'included angle'?

• Any angle in the triangle.

• The angle between the two proportional sides.

• The angle opposite the longest side.

• The smallest angle in the triangle.

When checking for SSS similarity, what should you do if the ratios of the sides are not equal?

• Check the angles instead.

• Recalculate the side lengths.

• Conclude that the triangles are not similar.

• Check for SAS similarity.

In the example given, what was the ratio of the sides for the first pair of triangles that were not similar?

• 0.75 and 0.75

• 0.75 and 0.71

• 0.71 and 0.75

• 0.71 and 0.71

What is the similarity statement for triangles ABC and RST when they are found to be similar by SSS?

• Triangle ABC is parallel to triangle RST

• Triangle ABC is similar to triangle RST

• Triangle ABC is congruent to triangle RST

• Triangle ABC is equal to triangle RST

In the SAS example, what was the common angle between the two triangles?

• 60 degrees

• 30 degrees

• 45 degrees

• 48 degrees

What must be true for triangles to be similar by either SSS or SAS?

• Sides must be equal and angles must be proportional.

• Sides must be proportional and angles must be congruent.

• Sides must be equal and angles must be parallel.

• Sides must be parallel and angles must be equal.