Exploring Adding and Subtracting Rational Expressions

What is required for two triangles to be considered similar under the angle-angle similarity theorem?

• Two corresponding sides are proportional

• All sides are congruent

• All angles are congruent

• Two corresponding angles are congruent

If triangle ABC has angles of 75 and 31 degrees, which other triangle could be similar by angle-angle similarity?

• Triangle with angles 60 and 30 degrees

• Triangle with angles 75 and 31 degrees

• Triangle with angles 75 and 59 degrees

• Triangle with angles 31 and 59 degrees

What does the side-side-side similarity theorem state about triangles?

• All corresponding sides are proportional

• All corresponding angles are congruent

• Two corresponding sides are proportional

• Two corresponding angles are congruent

How can you determine the similarity of triangles using the side-side-side theorem?

• Compare the proportion of the smallest to largest sides

• Compare the proportion of any two corresponding sides

• Ensure all sides are congruent

• Ensure all angles are congruent

What is the correct similarity statement for triangles with sides in the ratio 3:4:5 and 6:8:10?

• Triangle ABC ~ Triangle DEF

• Triangle MNO ~ Triangle PQR

• Triangle XYZ ~ Triangle RST

• Triangle QPR ~ Triangle TSU

What does the side-angle-side similarity theorem require for two triangles to be similar?

• Two angles congruent and any side proportional

• Two sides proportional and the included angle congruent

• All sides proportional

• All angles congruent

If triangle JKL has sides 8 and 6 with an included angle congruent to triangle MNP's included angle between sides 20 and 15, are they similar?

• Yes, by side-angle-side similarity

• No, the angles are not congruent

• No, the sides are not proportional

• Yes, by side-side-side similarity

In side-angle-side similarity, what is the importance of the included angle?

• It must be supplementary to the other angles

• It does not affect similarity

• It must be proportional to the sides

• It must be congruent to ensure similarity

How do you verify side-angle-side similarity if the sides are 25/15 and 21/12 with a congruent included angle?

• Check if the ratios reduce to the same fraction

• Ensure the sides are congruent

• Ensure the triangles are congruent

• Check if the angles are supplementary

Which statement is true about the side-angle-side similarity condition?

• It requires two proportional sides and one congruent angle

• It requires three congruent angles

• It requires two congruent angles and one proportional side

• It requires three proportional sides