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Lesson Design Subject Area: Geometry Grade Level: 9th – 12th Benchmark Period BM 3 Duration of Lesson: 2 days Standard(s): Geometry 4b: Prove basic theorems involving similarity. Learning Objective: Students will be able to identify similar triangles and prove two triangles are similar. Big Ideas involved in the lesson: Students will use similarity theorems to prove two triangles are similar. As a result of this lesson students will: Know: Vocabulary: Ratio, proportion, similar, similarity, congruent, corresponding, corresponding parts. Understand: If a and b are two quantities that are measured in the same units, then the ratio of a to b is a . b Ratio is a quotient. The denominator cannot be zero. An equation that equates two ratios is a proportion. Similar triangles: two triangles such that their corresponding angles are congruent and the lengths of their corresponding sides are proportional. Be Able To Do: Determine whether the triangles are can be proved similar. If triangles are similar, write a similarity statement. Assessments: What will be evidence of student knowledge, understanding & ability? Justify why the two triangles are similar. Anticipatory Set: a. T. focuses students b. T. states objectives c. T. establishes purpose of the lesson d. T. activates prior knowledge 1 Formative: Observation, quiz, ABWA Summative: CST & Benchmark (DWA) CFU Questions: 1. What is a conditional statement and how do you write conditional statements using similarity statement for angles, sides, and triangles? 2. What are the measurements of the other two angles? 3. What information do you need to complete the following three problems? Lesson Plan Hands on Geometry: Step 1: On a sheet of paper, use a ruler to draw a segment 2 cm in length. Label the endpoints A and B. Step 2: Use a protractor to draw an angle at A so that the measure of angle A equals 87°. Draw an angle at B so that the measure of angle B equals 38°. Extend the sides of angle A and angle B so that they intersect to form a triangle. Label the third vertex C. Step 3: Now draw a segment 4 cm in length. Label the endpoints D and E. Lesson Design Step 4: Use a protractor to draw an angle at D so that the measure of angle D equals 87°. °. Draw an angle at E so that the measure of angle E equals 38°. Extend the sides of angle D and angle E so that they intersect to form a triangle. Label the third vertex F. T. states, this lesson we will study two additional ways to prove that two triangles are similar, Side-Side-Side (SSS) Similarity Theorem, Side-AngleSide (SAS) Similarity Theorem, and Angle-Angle (AA) Similarity Postulate. T. reminds students they have learned how to use ratio and proportion to determine similarity numbers, units, etc. Instruction: a. Provide information Explain concepts State definitions Provide exs. Model b. Check for Understanding Pose key questions Ask students to explain concepts, definitions, attributes in their own words Have students discriminate between examples and nonexamples Encourage students generate their own examples Use participation Investigating Similar Triangles: Have students use whiteboard, to complete the following steps: Step 1: Use a protractor and a ruler to draw two non congruent triangles so that each triangle has a 40 degrees angle and a 60 degrees angle. Step 2: Measure the third angle, it will be 80 degrees. Step 3: Label one triangle as ∆ABC and the other as ∆DEF. Step 4: Measure the lengths of the sides of each triangle. Step 5: Write and simplify the ratios of the corresponding sides. T. explains: Similar triangles: two triangles such that their corresponding angles are congruent and the lengths of their corresponding sides are proportional. T. asks: Are the triangles similar? Discuss and justify as a class why the triangles are similar. T. states: The symbol to signify similar triangles is “~”. This activity are examples for Angle-Angle and Side-Side-Side. Angle-Angle (AA) Similarity Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Side-Side-Side (SSS) Similarity Theorem: If the corresponding sides of 2 triangles are proportional, then the triangles are similar. Side-Angle-Side (SAS) Similarity Theorem: If an angle of one triangle is congruent to an angle of a second triangle and the length of the side including these angles are proportional, then the triangles are similar. CFU: Write conditional statements using similarity statement for angles, sides, and triangles. Do class poster, record similarity statements. Guided Practice: a. Initiate practice activities under direct teacher 2 Refer to GeoCH0604example12.pps (use example 1) & GeoCH0605example12.pps. T. models how to solve problem 9 step-by-step along w/students at the same Lesson Design b. c. d. e. f. supervision – T. works problem step-by-step along w/students at the same time Elicit overt responses from students that demonstrate behavior in objectives T. slowly releases student to do more work on their own (semi-independent) Check for understanding that students were correct at each step Provide specific knowledge of results Provide close monitoring time. Have students work in pairs, and complete problems 10 & 11 on their whiteboards. CFU: Each student completes one of the two problems. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Have students work in pairs, and complete problems 5 & 6 on their whiteboards. CFU: Each student completes one of the two problems. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. CFU: Have students continue to work in pairs, but do their own work on a separate sheet of paper. Complete the following three problems. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. What opportunities will students have to read, write, listen & speak about mathematics? Closure: a. Students prove that they know how to do the work b. T. verifies that students can describe the what and why 3 Students will be answering questions, writing notes and problems, describing the process to the teacher and their peers, and reading problems. Based on SSS and SAS theorems and AA postulate, and two given triangles. Write how each of the rules proves triangles are similar? Lesson Design of the work c. Have each student perform behavior Independent Practice: a. Have students continue to practice on their own b. Students do work by themselves with 80% accuracy c. Provide effective, timely feedback Assign the following problems. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Resources: materials needed to complete the lesson 4 Whiteboard, protractor, ruler, poster paper