Geometric Proofs Challenge

This video tutorial introduces geometric proofs, focusing on two-column proofs. It explains the structure of these proofs, including statements and reasons, and demonstrates how to use given information, postulates, theorems, and properties. Three examples are provided: the first uses the angle addition postulate, the second involves segment addition and substitution, and the third demonstrates angle subtraction. Each example illustrates how to construct a proof step-by-step, emphasizing the logical flow and application of mathematical properties.

What are the two columns in a two-column proof used for?

• Reasons and conclusions

• Statements and conclusions

• Hypotheses and conclusions

• Statements and reasons

What can be used as reasons in a geometric proof?

• Only theorems and properties

• Only given information

• Only postulates

• Given information, postulates, theorems, properties, definitions, or corollaries

In the first example, what postulate allows you to add two smaller angles to equal a larger angle?

• Angle division postulate

• Angle multiplication postulate

• Angle addition postulate

• Angle subtraction postulate

What property is used when replacing a quantity with an equal quantity in a proof?

• Substitution property

• Transitive property

• Addition property

• Reflexive property

In the second example, which property states that a segment is equal to itself?

• Substitution property

• Addition property

• Transitive property

• Reflexive property

What property is used when adding equal quantities to both sides of an equation?

• Division property

• Addition property

• Subtraction property

• Multiplication property

In the second example, what is the result of adding FL and LA?

• Segment FA

• Segment LA

• Segment LT

• Segment FL

In the third example, what is the measure of a straight angle?

• 360 degrees

• 180 degrees

• 45 degrees

• 90 degrees

What property allows you to remove the same angle from both sides of an equation?

• Substitution property

• Reflexive property

• Subtraction property

• Addition property

In the third example, what is the final conclusion after removing angle 4 from both sides?

• Angle 5 is equal to angle 4

• Angle 4 is equal to angle 5

• Angle 5 is equal to angle 6

• Angle 6 is equal to angle 4