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Fill in the missing statements and reasons in the proof

Fill in the missing statements and reasons in the proof 2026

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The document is a practice worksheet for CCGPS Geometry focusing on congruence and triangles. It includes problems that require students to fill in missing statements or reasons to prove the congruence of triangles using various geometric theorems and properties.

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Begin with Problem 1. Identify the given information: CB  AD and CB || AD. Use the provided statements bank to fill in the missing reasons for proving that BCD  DAB.
For each statement, select the appropriate reason from the bank, such as 'Corresponding angles are congruent' or 'SAS', ensuring you understand how each applies to your proof.
Proceed to Problem 2. Note that WOK is isosceles and Point R is the midpoint of WK. Again, refer to the statements bank to complete your proof for OWR  OKR.
Continue this process for Problems 3 and 4, carefully selecting reasons that align with your given information and conclusions.

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Which of the following can be used as reasons in a proof?

The missing reason for the 5th step in the proof is likely the Substitution Property, which allows for replacing a variable with its equal value.

What is statement and reason?

Statements are different from Reasoning in that statements are facts and are said with a tone showing facts. Reasoning, however, is statements that seek to link particular evidence to a claim, i.e., Reasoning provides valid proof of why a particular claim is true.

What is the purpose of statements and reasons in a formal proof?

The following reasons may be used in order to prove a logical argument true: Given information: any provided information within the proof. Definitions: any known mathematical definitions. Axioms: abstractly defined statement. Postulates: an assumed truth or obvious statement. Theorems: logical statement proven true.

What are the four things we use for reasons in proofs?

Each statement in a proof follows from one or more of the previous statements. A reason for a statement can come from the set of given premises or from one of the four types of other premises: definitions; postulates; properties of algebra, equality, or congruence; or previously proven theorems.

What does a formal proof need to have?

A formal proof is a series of statements. Each statement must either be a hypothesis (assumption) or follow from previous statements in the proof and previously proven theorems. The proof must end with a statement that is either the intended conclusion or that trivially implies the intended conclusion.