Exploring SSS and SAS Similarity Theorems in Triangles

This video tutorial continues the unit on similarity, focusing on the side-side-side (SSS) and side-angle-side (SAS) similarity theorems. It explains how to determine if triangles are similar by comparing the ratios of their sides and angles. The tutorial includes examples of applying these theorems to find unknown side lengths and verify triangle similarity. The video concludes with a summary and contact information for further questions.

What does the angle-angle similarity theorem state?

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

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

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

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

What is the key difference between the side-side-side similarity theorem and the side-side-side congruence theorem?

• Similarity theorem requires proportional angles, congruence theorem requires equal angles.

• Similarity theorem requires proportional sides, congruence theorem requires equal sides.

• Similarity theorem requires equal sides, congruence theorem requires proportional sides.

• Similarity theorem requires equal angles, congruence theorem requires proportional angles.

If the ratios of corresponding sides of two triangles are equal, what can be concluded?

• The triangles have equal angles.

• The triangles are similar.

• The triangles are congruent.

• The triangles are neither similar nor congruent.

In the example comparing triangle ABC to triangle DEF, what is the ratio of the shortest sides?

• 3/2

• 4/3

• 3/4

• 2/3

What should you do if one ratio of corresponding sides does not match when checking for similarity?

• Recalculate the ratios.

• Check the angles instead.

• Stop, as the triangles are not similar.

• Continue checking the other sides.

How do you set up a proportion to find the value of x that makes two triangles similar?

• Use only the sides with known lengths.

• Use the angles of the triangles.

• Use three sides where one side has the value of x.

• Use any two sides of the triangles.

What is the value of x that makes triangle XYZ similar to triangle HJK in the given example?

• 11

• 9

• 13

• 7

What is required for two triangles to be similar according to the side-angle-side similarity theorem?

• Two sides must be proportional and the included angle must be congruent.

• Two sides and the included angle must be congruent.

• All three sides must be proportional.

• All three angles must be congruent.

In the example of the triangular roof truss, why are the two triangles not similar?

• The triangles are not right-angled.

• The sides are not proportional.

• The angles are not congruent.

• The sides are not equal.

What is the final step to confirm that two triangles are similar using the side-angle-side similarity theorem?

• Check if the sides are equal.

• Check if the angles are congruent.

• Check if the sides are proportional and the included angle is congruent.

• Check if the triangles are right-angled.