Exploring Adding and Subtracting Rational Expressions

The video tutorial covers theorems of similarity, focusing on angle-angle, side-side-side, and side-angle-side similarity. It provides examples and exercises to determine triangle similarity using these theorems, emphasizing the importance of congruent angles and proportional sides.

What theorem is used to determine the similarity of triangles based on two congruent angles?

• Side-Side-Side theorem

• Angle-Angle similarity

• Side-Angle-Side theorem

• Angle-Side-Angle theorem

If two triangles have two sets of corresponding angles congruent, are they similar?

• Only if the sides are proportional

• No, never

• Yes, always

• Only if they are right triangles

What is required to prove triangle similarity using the Side-Side-Side theorem?

• Two sides proportional and one angle congruent

• All three sides proportional

• Two angles congruent

• One side and two angles congruent

How do you determine the decimal ratio for side lengths when checking for Side-Side-Side similarity?

• Subtract the corresponding side lengths

• Divide the corresponding side lengths

• Add the lengths

• Multiply the lengths

What is the correct similarity statement for triangles with proportional sides of 9, 13.5, and 20.25 in one triangle and 14, 21, and 31.5 in another?

• Triangle GHI is similar to triangle JKL

• Triangle ABC is similar to triangle DEF

• Triangle STU is similar to triangle VWX

• Triangle MNO is similar to triangle PQR

In the Side-Angle-Side similarity, what must be true about the angle included between the two sides?

• It must be obtuse

• It must be right

• It must be congruent in both triangles

• It must be acute

Can triangles be similar if only one pair of corresponding angles is congruent?

• Yes, always

• Only if the other angles are also congruent

• No, never

• Only if the sides are proportional

What is the result of comparing side ratios of 15/45 and 14/42 in the context of Side-Angle-Side similarity?

• They are congruent

• They are similar

• They are complementary

• They are not similar

What happens if the included angles in a Side-Angle-Side scenario are not congruent?

• The triangles are still similar

• The triangles are not similar

• The triangles are congruent

• The triangles are identical

In a Side-Angle-Side comparison, if the side ratios are 50/35 and 45/31.5, what can be inferred about the triangles?

• They are identical

• They are congruent

• They are not similar

• They are similar