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Proving Statements about Segments

Proving Statements about Segments. Goal 1: Justify statements about congruent segments. In the previous section, you learned how to use the properties o f equality to prove statements. In this section, we will learn a bout the properties of congruence and how to use them to

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Proving Statements about Segments

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  1. Proving Statements about Segments Goal 1: Justify statements about congruent segments

  2. In the previous section, you learned how to use the properties of equality to prove statements. In this section, we will learn about the properties of congruence and how to use them to prove statements about segments. Properties of Segment Congruence: (put in Theorems section of notebook) Reflexive Property of Congruence: AB = AB Symmetric Property of Congruence: Transitive Property of Congruence:

  3. Two Column Proofs Statments Reasons .P .X EXAMPLE: We can use the Properties of Equality to prove the Properties of Congruence. Prove the Symmetric Property of Congruence as follows: Given line segment PQ = XY. Prove line segment XY = PQ. .Q .Y Given Def of Congruent Segments Sym Prop of = Def of Congruent Segments

  4. K Example 2: Given LK = 5, JK = 5, JK = JL Prove LK = JL J L LK = 5 1. Given 2. Given 3. 3. Trans Prop of = 4. 4. Def of___________ 5. 5. Given 6. 6. Trans Prop of Congruence JK = 5 LK = JK LK = JK Congruent Segments JK = JL LK = JL Remember: When writing a reason for a step in a Proof, you must use: given info, a definition, a property, a postulate or a previously provern theorem

  5. Example 3: Given Q is the midpoint of PR Prove PQ = ½ PR and QR = ½ PR Q is midpoint of PR PQ = QR PR = PQ + QR PR = PQ + PQ PR = 2PQ PQ = ½ PR QR = ½ PR Given Def of mdpt Seg + Post Sub = Distributive Prop = Division Prop = Sub Prop =

  6. Solve for the variable using the given information. Explain each step. Example: Given AB = BC, CD = BC AB = 2x + 1, CD = 4x - 11 .A .B .C .D Given 1. AB = BC, CD = BC Trans Prop = 2. AB = CD Given 3. AB = 2x + 1, CD = 4x - 11 Sub 4. 2X + 1 = 4X - 11 - Prop = 5. 1 = 2x -11 + Rrop = 6. 12 = 2x Div Prop = 7. X = 6

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