Geometry Proofs: Mastering Basic Techniques

This video tutorial by Mark Kara demos on mathguide.com introduces the basics of doing proofs in geometry. It explains the structure of proofs, which involves statements and reasons, and provides examples of proofs involving angle bisection and midpoint congruence. The tutorial emphasizes the importance of using given information and definitions to justify statements and warns against making assumptions based on the appearance of diagrams.

Why is it recommended to create a diagram if one is not provided?

• To make the problem look more complex

• To visualize the problem and understand it better

• To make the proof longer

• To add more information to the problem

What are the two columns used in a proof?

• Statement and Diagram

• Reason and Diagram

• Statement and Reason

• Proof and Conclusion

What is the first step in writing a proof?

• Write the conclusion

• Draw a diagram

• Write down the given information

• List all possible reasons

What does it mean for a segment to bisect an angle?

• To divide the angle into three equal parts

• To cut the angle in half

• To make the angle larger

• To remove the angle

If segment EG bisects angle DEF, what can be said about the two resulting angles?

• They are complementary

• They are right angles

• They are congruent

• They are supplementary

What is the definition of a midpoint in a segment?

• A point that is at the end of the segment

• A point that divides the segment into two equal parts

• A point that divides the segment into two unequal parts

• A point that is outside the segment

If J is the midpoint of segment KM, what can be said about segments JK and JM?

• JK and JM are perpendicular

• JK and JM are congruent

• JK is shorter than JM

• JK is longer than JM

What property allows us to say that vertical angles are congruent?

• Definition of midpoint

• Definition of bisect

• Vertical angles theorem

• Reflexive property

Which of the following is NOT a valid reason in a proof?

• Given information

• Definition of bisect

• It looks like it

• Vertical angles theorem

What should be done if a diagram looks like a specific shape but it is not given?

• Only use properties that are given or can be proven

• Ignore the diagram

• Assume it is that shape

• Change the diagram