Proving Angle and Segment Relationships in Geometry
In this geometry lesson, students will engage in writing simple algebraic proofs using angle and segment addition postulates. They will explore concepts such as the Angle Addition Postulate and the Segment Addition Postulate, which are essential for establishing relationships between angles and line segments. The lesson includes examples illustrating how to prove equal angles and segments, making use of algebraic reasoning. Students will also have a homework assignment to reinforce their understanding of angle and segment addition fundamentals.
Proving Angle and Segment Relationships in Geometry
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Presentation Transcript
Daily Warm-Up Geometry
Daily Warm-Up Given: m 1 = m 3 Prove: m 1 + m 2 = m 2 + m 3 Geometry
Reasoning in Algebra During this lesson, you will write simple algebraic proofs using angle and segment addition postulates. Geometry
Recall: Angle Addition Postulate If D is in the interior of ∠ ABC, then _____________________. A D B C Geometry
Recall: Segment Addition Postulate If M is between collinear points A and Y, then ______________. AM + MY = AY Y M A Geometry
Example 1 Given: m ∠ DOF = 124, m ∠ DOE = 36. Find m ∠ EOF. O D E F Geometry
Labeling Angles Using Numbers C D B ∠ 1 = _____ ∠ 2 = _____ ∠ 3 = _____ A 2 3 1 O Geometry
Reflexive Property of Congruence A A and AB AB for any angle A and any segment AB. You will use the reflexive property in many proofs. Geometry
Example 2: Writing a Simple Proof Given: m ∠ 1 = m ∠ 3 Prove: m ∠ WOY = m ∠ ZOX Z Y X 3 2 W 1 Geometry
Example 3: Writing a Simple Proof Given: AB = CD Prove: AC = BD D C B A Geometry
Homework Assignment Supplemental WS: Angle and Segment Addition 1-17 all. Geometry
