Proving Triangle Congruence with Two Column Proofs

The video tutorial guides students through writing a geometric proof using a two-column format. It begins with setting up the proof by identifying given statements and premises. The tutorial then explores congruency and the reflexive property, followed by examining angle relationships with parallel lines and transversals. Finally, it demonstrates how to complete the proof using angle-angle-side congruency, ensuring the correct order of corresponding angles and sides.

What is the first step in writing a two-column proof?

• Draw the figure

• Write down the given statements

• List all possible theorems

• Identify the conclusion

Why do we know that DE is parallel to FG?

• Because they form a right angle

• Because it is given

• Because they are perpendicular

• Because they are equal in length

Which angles are given as congruent in the problem?

• Angle D and Angle F

• Angle E and Angle G

• Angle F and Angle G

• Angle D and Angle E

What are the two congruence criteria practiced in the homework?

• Angle-Side-Angle and Side-Side-Side

• Angle-Side-Angle and Angle-Angle-Side

• Side-Angle-Side and Angle-Angle-Side

• Side-Side-Side and Side-Angle-Side

What property allows us to say that line DE is congruent to line ED?

• Transitive Property

• Reflexive Property

• Symmetric Property

• Substitution Property

What should you always look for when you see parallel lines in a proof?

• Midpoints

• Congruent sides

• Angle relationships

• Perpendicular bisectors

Which angle relationship is used when two angles are interior of the parallel lines and alternate the transversal?

• Alternate interior angles

• Alternate exterior angles

• Same side interior angles

• Corresponding angles

What is the final statement in a proof supposed to be?

• The given statements

• The conclusion you are trying to prove

• The reasons for each step

• The figure of the problem

Why are angles EDF and GFD congruent?

• Because they are corresponding angles

• Because they are alternate interior angles

• Because they are supplementary angles

• Because they are vertical angles

Which congruence criterion is used to prove that triangle DFG is congruent to triangle FDE?

• Side-Angle-Side

• Angle-Side-Angle

• Angle-Angle-Side

• Side-Side-Side