Introduction to Proofs and Properties of Congruence

This video introduces the concept of proofs in mathematics, focusing on two-column proofs using properties of congruence. It explains the reflexive, symmetric, and transitive properties of congruence for segments and angles. The video provides examples of two-column proofs, demonstrating how to prove segment and angle congruence using given information, the addition property, and substitution. The video concludes with a promise of more examples in future videos.

What is the primary method used to obtain proofs in mathematics?

• Deductive reasoning

• Empirical observation

• Inductive reasoning

• Statistical analysis

Tags

CCSS.HSG.CO.C.10

What is a statement called once it has been proven?

• Theorem

• Postulate

• Conjecture

• Hypothesis

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CCSS.HSG.SRT.B.5

Which property of congruence allows changing the order of endpoints in segments?

• Reflexive property

• Symmetric property

• Associative property

• Transitive property

Tags

CCSS.HSG.CO.C.10

If segment AB is congruent to segment CD, and segment CD is congruent to segment EF, which property states that segment AB is congruent to segment EF?

• Transitive property

• Distributive property

• Reflexive property

• Symmetric property

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CCSS.HSG.SRT.B.5

In a two-column proof, what is the purpose of the right column?

• To summarize the proof

• To provide reasons or justifications

• To list the given information

• To state the conclusion

What property is used when stating AE + EB = CE + ED in a proof?

• Division property

• Addition property of equality

• Multiplication property

• Subtraction property

Tags

CCSS.4.MD.C.7

Which property allows the substitution of equal segments in a proof?

• Reflexive property

• Symmetric property

• Transitive property

• Substitution property

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CCSS.4.MD.C.7

What is the goal when using the angle addition property in a proof?

• To find the measure of a single angle

• To prove two angles are congruent

• To add the measures of two angles

• To subtract the measures of two angles

Tags

CCSS.4.MD.C.7

What property is used to conclude that the measure of angle 1 equals the measure of angle 3?

• Addition property of equality

• Subtraction property of equality

• Multiplication property of equality

• Division property of equality

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CCSS.RI.11-12.3

CCSS.RI.8.3

CCSS.RI.8.5

CCSS.RI.9-10.3

CCSS.RI.9-10.5

What will future videos focus on according to the conclusion?

• Introduction to algebraic proofs

• Basic arithmetic operations

• More examples of two-column proofs

• Advanced calculus problems

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CCSS.RI.7.5

CCSS.RI.8.3

CCSS.RI.8.5

CCSS.RI.9-10.3

CCSS.RI.9-10.5