Proving Triangle Similarity with SSS and SAS

This video tutorial covers the methods to prove triangle similarity using theorems such as SSS, SAS, and AA. It includes detailed explanations of these theorems, followed by example problems to illustrate their application. The tutorial also provides advanced examples and practice problems, focusing on comparing multiple triangles and using proportions to find missing side lengths. The session concludes with a task for students to apply their learning by solving additional problems.

What does it mean for two triangles to be similar?

• All sides are proportional and one angle is congruent.

• All sides are equal and one angle is congruent.

• All angles are congruent and all sides are equal.

• All angles are congruent and all sides are proportional.

Which theorem states that two triangles are similar if all three pairs of sides are proportional?

• AA

• ASA

• SSS

• SAS

In the SAS theorem for triangle similarity, what must be true about the angles?

• The included angles must be congruent.

• No angles need to be congruent.

• All angles must be congruent.

• One angle must be congruent.

If two triangles have sides in the ratio 3:4, 6:8, and 9:12, are they similar?

• No, the angles are not congruent.

• Yes, by SAS similarity.

• No, the sides are not proportional.

• Yes, by SSS similarity.

In the example where the sides of the first triangle are 6, 9, and 12, and the sides of the second triangle are 8, 12, and 16, what is the ratio of the smallest sides?

• 3/2

• 2/3

• 4/3

• 3/4

What is the similarity statement for triangles GHJ and IJK if GHJ is similar to IJK?

• GHJ ~ JKI

• GHJ ~ IJK

• GHJ ~ IKJ

• GHJ ~ KJI

If two triangles have sides in the ratio 4:5, 8:10, and 12:15, are they similar?

• No, the angles are not congruent.

• Yes, by SAS similarity.

• No, the sides are not proportional.

• Yes, by SSS similarity.

In the example where the sides of the left triangle are 12, 16, and 20, and the sides of the right triangle are 9, 12, and 15, what is the ratio of the smallest sides?

• 4/3

• 3/4

• 2/3

• 3/2

What are the values of x and y that make triangle PHS similar to triangle GEO?

• x = 5, y = 8

• x = 8, y = 11

• x = 6, y = 9

• x = 7, y = 10

What should you do if you encounter problems while comparing triangles for similarity?

• Skip the problem.

• Refer back to the first page of notes.

• Ask a friend for help.

• Guess the answer.