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Illustrating Theorems on Triangle presentation
- 1. Author: Pi Date:202X.XX.XX Illustrating Theorems on Triangle Inequalities
- 2. 4. Assessment 1. Objectives2. Lesson Proper 3. Integration Application: Engineering and Architecture CONTENTS
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- 4. 2 1 Longest Sideand Largest Angle • Explore the relationship between the longest side and the largest angle in a triangle. • Investigate the relationship between the sum of any two sides and the remaining side in a triangle. Investigate Relationships in Triangles Sum of Sides
- 5. • Exterior AngleInequality Theorem • Triangle Inequality Theorem • Hinge Theorem and its converse Triangle Inequalities Illustrate Theorems
- 6. Connect theorems intriangle inequalities to real-life settings. Real-Life Connections
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- 8. 1 3 2 • Whyare relationships important in understanding structures? Motivation Learning Targets • Determine relationships between angles and sides of a triangle. • Apply triangle inequalities to solve real-life problems. Essential Question Introduction (5 minutes) • Present real- world structures (e.g., bridges, roofs, support beams) and discuss stability through triangular formations.
- 9. • Protractor, ruler Interaction(30 minutes) Activity A: Investigate Me! • Directions: Use the figure below to answer the questions that follow. Write your answer on a separate sheet of paper. • What is the included side in B and C? in E and F? ∠ ∠ ∠ ∠ • What is the included angle in and ? in and ? 𝐴𝐶̅̅̅̅ 𝐵𝐶̅̅̅ 𝐷𝐹̅̅̅̅ 𝐸𝐹̅̅̅̅ • What is the sum of the interior angles of ABC? ∆ DEF? ∆ • If B E, and C F, ∠ ≅ ∠ ∠ ≅ ∠ Activity B: Materials Needed
- 10. 2 3 5 14 Angle-Side Relationshi p Theorem Discussion • The sum of the lengths of any two sides Converse of Hinge Theorem or SSS Inequality Theorem Triangle Inequality Theorem • An exterior angle is • Larger angle Hinge Theorem or SAS Inequality Exterior Angle Inequality Theorem • If two sides of one
- 11. 3. Integration Application: Engineeringand Architecture
- 12. Output Evaluation Criteria •Designing a bridge with triangular supports. 3. Integration Application: Engineering and Architecture • Neatness, mathematical accuracy, and logical explanation. Task • Sketch triangular supports, label sides and angles, and justify design using triangle inequality theorems. Scenario
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- 14. 4. Assessment • Directions:Write your answer on a separate sheet of paper. Am I a Triangle? • Directions: Determine if the following lengths can form a triangle. Use ( ) for yes and (X) for ∆ no. • 1, 2, 3 • 17, 16, 9 • 9, 11, 18 • 4, 8, 11 • 5, 13, 6 Identify Me
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