Introduction to Proof Answers

Which property is shown?If m∠ABC = m∠CBD, then m∠CBD = m∠ABC reflexive propertysubstitution propertysymmetric propertytransitive property

What statements are true regarding the given statement and diagram?

A:

A:

division definition of bisects definition of right angle ✔ given

Identify the missing parts in the proof.

Sample Response: One type of proof is a two-column 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. What did you include in your response? Check all that apply.Two-column proofs are in columns and list statements and reasons.Paragraph proofs use words.Flowchart proofs give a visual representation of the progression of

✔ definition of congruent definition of bisect given reflexive property

Sample Response: 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. What did you include in your response? Check all that apply.given informationstatement to be provenargument with justification using theorems, definitions, and axiomsconclusion

identity propertyreflexive property ✔ substitution propertysymmetric property

✔ measure of angle ABC = 90measure of angle ABC = 180measure of angle ABD = 90 measure of angle CBD = 180

Sample Response: We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A. What did you include in your response? Check all that apply.reflexive propertysubtr

definition of congruent ✔ definition of bisect given reflexive 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