Introduction to Proof Answers
Which property is shown?If m∠ABC = m∠CBD, then m∠CBD = m∠ABC
What statements are true regarding the given statement and diagram?
definition of congruent definition of bisect ✔ given reflexive property
45✔ 90180360
✔ definition of right angledefinition of congruentdefinition of equaldefinition of 90 degrees
division definition of bisects definition of right angle ✔ given
Given: m∠A + m∠B = m∠B + m∠CProve: m∠C = m∠AWrite a paragraph proof to prove the statement.
It is given that m∠A m∠B m∠B m∠C. According to the subtraction property of equality, the same value can be subtracted from both sides of an equation without changing the equality. By subtracting m∠B from both sides of the equation, the result is m∠A m∠C. By the symmetric property of equality, if m∠A m∠C, then m∠C m∠A.
Name the three different types of proofs you saw in this lesson. Give a description of each.
One type of proof is a twocolumn proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.
Describe the main parts of a proof.
Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.
✔ definition of congruent definition of bisect given reflexive property
AEB ✔ AEC BEC BED
identity propertyreflexive property ✔ substitution propertysymmetric property
✔ measure of angle ABC = 90measure of angle ABC = 180measure of angle ABD = 90 measure of angle CBD = 180
What did you include in your response? Check all that apply.
What did you include in your response? Check all that apply.
What did you include in your response? Check all that apply.
definition of congruent ✔ definition of bisect given reflexive property
✔ angle addition postulate reflexive property segment addition property symmetric property
✔ definition of congruent angles definition of equal angles substitution property symmetric property
addition✔ angle addition postulate definition of right anglesubstitution property
angle ABC = 90 angle ABD = 90 2 times the measure of angle ABC = 90 ✔ 2 times the measure of angle CBD = 90
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