1 / 6

Understanding Segment Congruence: Proving Statements with Inequalities and Theorems

This section focuses on justifying statements about congruent segments using the properties of congruence and equality. Key properties include the Reflexive, Symmetric, and Transitive Properties of Congruence. Learn how to apply these concepts through two-column proofs and examples. Detailed steps illustrate how given information, definitions, and theorems anchor the reasoning in proofs. By the end, you'll understand how to prove relationships between segments, such as congruence and midpoints, equipping you with essential skills in geometry.

mechelle-george
Télécharger la présentation

Understanding Segment Congruence: Proving Statements with Inequalities and Theorems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related