Triangle Congruence Proofs Challenge

What is the purpose of a two-column proof in geometry?

• To measure angles

• To draw geometric shapes

• To solve algebraic equations

• To list out steps and reasons to prove statements

In a two-column proof, what do the 'givens' represent?

• The reasons for each step

• The final conclusion

• The initial known facts

• The steps to be proven

Why are vertical angles always congruent?

• Because they are adjacent

• Because they are opposite each other

• Because they are supplementary

• Because they are complementary

What does the reflexive property state in geometry?

• Two triangles are similar

• Two sides are parallel

• A side is congruent to itself

• Two angles are equal

Which congruence criterion is used when two angles and a non-included side are known?

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

• Side-Angle-Side (SAS)

What does a bisector do in a geometric figure?

• Divides a line segment into two equal parts

• Divides an angle into two equal parts

• Forms a right angle

• Creates a perpendicular line

How does the definition of a midpoint help in proving triangle congruence?

• It shows that two triangles are similar

• It shows that two angles are equal

• It shows that two sides are equal

• It shows that two lines are parallel

What is the first step in any two-column proof?

• Determine the congruence criterion

• Identify the vertical angles

• Write down the givens

• Mark the reflexive property

Which theorem states that all right angles are congruent?

• Reflexive Property

• Right Angle Congruence Theorem

• Angle-Side-Angle (ASA) Theorem

• Vertical Angles Theorem

What is the final goal in a two-column proof?

• To find the vertical angles

• To list all the steps

• To prove the triangles are congruent

• To identify the givens