Exploring Adding and Subtracting Rational Expressions

What does the SSS (side-side-side) congruence theorem state?

• If all three sides of one triangle are congruent to all three sides of another triangle, the triangles are congruent.

• If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

• If all three angles of one triangle are congruent to all three angles of another triangle, the triangles are congruent.

What is the first step in writing a proof for triangle congruence?

• Mark the diagram with given information.

• Determine the midpoint of a side.

• Write the final congruence statement.

• Identify the reflexive property.

Why is it important to mark the diagram when writing a proof?

• To avoid writing too much text.

• To confuse the reader.

• To visually see and understand the relationships between the given information.

• To make the proof look more colorful.

What does the reflexive property state?

• Two angles of a triangle are congruent to each other.

• A triangle is congruent to another triangle with the same area.

• A side of a triangle is congruent to the corresponding side of another triangle.

• A side of a triangle is congruent to itself.

In the context of triangle congruence, what does the term 'midpoint' refer to?

• The point that is the center of a circle inscribed in a triangle.

• The point that is equidistant from all vertices of a triangle.

• The point that divides a segment into two congruent segments.

• The point where two triangles intersect.

What is the key requirement for the SAS (side-angle-side) congruence theorem?

• The sides must be parallel.

• The sides must be of equal length.

• The angle can be any angle in the triangle.

• The angle must be between the two sides being compared.

Which of the following is NOT a valid congruence theorem?

• SSA (side-side-angle)

• SSS (side-side-side)

• SAS (side-angle-side)

• ASA (angle-side-angle)

What should you do if you cannot derive any more information from the given statements in a proof?

• Ask someone else for help.

• Start over from the beginning.

• Look at the diagram for additional clues.

• Guess the next step.

What is the purpose of the 'included angle' in the SAS theorem?

• It is the angle between the two sides being compared.

• It is the angle opposite the longest side.

• It is the angle that is congruent to the corresponding angle in another triangle.

• It is the angle formed by the intersection of two triangles.

Why is it important to understand different congruence theorems?

• To make geometry proofs more colorful.

• To solve complex geometry problems efficiently.

• To avoid using diagrams in proofs.

• To confuse the reader with multiple theorems.