Sheet1GENERAL SANTOS HOPE CHRISTIAN SCHOOLBlock 5, Dadiangas HeightsGeneral Santos City, PhilippinesGEOMETRY George L. LimYear Level: HS 3Lesson Topic:ParallelismLength of Lesson:18 SessionsStage 1 - Desired Results1.Identify parallel and skew lines, parallel planes, transversal, and the angles formed by them.2.Prove and apply the theorem about the intersection of two parallel planes by a third plane.3.State the Parallel Postulate4.Prove and use theorems relating parallel lines and angles formed by a transversal of those lines.5.Classify triangles by sides and angles.6.Prove and apply the theorems regarding angle measure and angle relationships in a triangle.7.Recognize and name convex, concave and regular polygons and find the measures of the interior and exterior angles of a convex polygon.Stage 2 - Assessment EvidenceUnderstanding(s)/goals:Essential Question(s):Students will understand:* Where can the concepts of parallel lines, * the concept of angles formed by the intersection intersecting lines, and skew lines be found in our of transversals and parallel lines. surrounding? * that parallel lines appear in many different * How was the concept of parallel lines used in instruments. science and technology? * the relationships of angles in triangles and other polygons.* How can a regular polygon be modified?* What angle relationships can be formed when a transversal intersects parallel line?* How can a regular polygon be modified?

Student will know * the parallel and skew lines, parallel planes,Student will be able to transversals and angles formed by them. * identify parallel, skew, and transversal lines. * the theorems, postulates, and corollaries * Classify triangles by sides and angles., involving parallel lines, perpendicular lines and recognize and name convex, concave, and regular triangles. polygons. * the different shape of polygons * find the measures of the interior and exterior angles of a convex polygon. * write a two column proof, given a situation, involving parallel, transversal lines, and triangles.

Stage 2 - Assessment EvidencePerformance Task(s):Other Evidence:Group Activity 1Answer investigation on page 80.Oral report in class of the results of the performance task.Group Activity 2Seatwork/HomeworkAnswer investigation on page 85.

Group Activity 3Quizzes/ Mastery testAnswer investigation on page 95.

Group Activity 4Answer investigation on page105

Group Activity 5Answer investigation on page 114.

Rubric:4 - Excellent, 3 - Good, 2 - Competent, 1 - Needs Improvement 0 - Needs Help

Level 4:Shows full understanding in writing formal proof with correct justification.Shows proficiency in knowledge of parallel lines and angles of polygon.Level 3:Shows understanding in writing formal proof but with few mistakes.Shows proficiency in knowledge of parallel lines and angles of polygon.Level 2:Shows partial understanding in writing formal proof with lots of mistakes.Lacks proficiency in knowledge of parallel lines and angles of polygon.Level 1:Lacks understanding in writing formal proof and lacks proficiency in knowledge of parallel lines and angles of polygon.Level 0:Confused. Does not know how to start writing a formal proof.Poor knowledge of parallel lines and angles of polygon.

Stage 3 - Learning PlanLearning Activities:3.1 Lines, Planes, and Transversal This lesson introduces many new terms. Tell students theSession 1 terminology will be used in the next lesson. Use parts of the classroom as models for terms in this lesson. Ask students to classify lines as parallel, intersecting, or skew.

Seatwork/QuizSession 2

3.2 Properties of Parallel LinesSession 3 Have students draw two prallel lines, draw a trasversal, and measure the eight angles formed. Ask them what they have discovered. To reinforce the structure of geometry, emphasize that postulate 11 is uded to prove the theorems in this lesson. Discuss the hypothesis and conclusion of each postulate and theorem presented in this lesson Many students will still have trouble writing formal proof. Help students to reason from the hypothesis to the conclusion.

Seatwork/QuizSession 4

3.3 Proving Lines Parallel Discuss the hypothesis and coclusion of each postulate andSession 5 theorem. Have students analyze the relationship between the postulates and theorems of this lesson and those of previous lesson. Have students justify their conclusiosn by identifying the reasons that enable them to determine whether or not given lines are parallel.

Seatwork/QuizSession 6

3.4 Parallel Lines and TrianglesSession 7 Some students will recall from earlier courses that the sum of the measures of the angles of a triangle is 180, and not see the need to prove the stement. Remind them that our geometric structure is based on definitions, postulates, and theorems. Help students plan proofs of the corollaries.

Seatwork/QuizSession 8

3.5 Strategy: Use Auxiliary LinesSession 9 Draw a hexagon and challenge the students to suggest auxiliary lines or segments to draw to determine the sum of the measures of the angles. Emphasize that students must be able to justify the existence of any auxiliary figure introduced. Students often have difficulty in determining how and where to use auxiliary figures. As they work out the Plan of a proof, help them to determine what additional information could lead them from the Given to the Prove.

Seatwork/QuizSession 10

3.6 PolygonsSession 11 Ask student if they can draw a triangle that is equilateral but not equiangular, or a triagle that is equiangular but not equilateral. (answer: not possible) Ask students to draw a four-sided figures that are: 1. equiangular and equilateral2. equilateral but not equiangular3. equangular but not equilateral Direct students to examine certain differences between triangles and quadrilaterals. Ask students to produce and identify examples of regular equilateral and equiangular quadrilatersls.

Seatwork/QuizSession 12

3.7 Strategy: Use Inductive ReasoningSession 13 Induction is sometimes described as reasoning from the specific to the general - by examining a number of specific cases, a generalization about all such objects is reached. Remind students that faulty conclusion can result from inductive reasoning. Ask students to distinguish between inductive and deductive reasoning and roles played by each type of reasoning in mathematics.

Seatwork/QuizSession 143.8 Angles of a Polygon Point out that if a student needs to find the measure of an interior angle of a regular polygon (or the sum of the interior angles) and can't recall the formula, the answer can be calculated if the students recalls that the sum of the measures of the exterior angles, one at each vertex, is always 360.

Seatwork/QuizSession 15

Mastery TestSession 16/17

Review Mastery TestSession 18

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