Illustrating Theorems on Triangle presentation

Mathematics 8 - Illustrating Theorems on Triangle

1. Author: Pi Date: 202X.XX.XX Illustrating Theorems on Triangle Inequalities

2. 4. Assessment 1. Objectives 2. Lesson Proper 3. Integration Application: Engineering and Architecture CONTENTS

3. 1. Objectives

4. 2 1 Longest Side and 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 Angle Inequality Theorem • Triangle Inequality Theorem • Hinge Theorem and its converse Triangle Inequalities Illustrate Theorems

6. Connect theorems in triangle inequalities to real-life settings. Real-Life Connections

7. 2. Lesson Proper

8. 1 3 2 • Why are 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. • Measure angles opposite given lengths using a protractor and record in a table. • Discover the relationship between side lengths and opposite angles and document findings. • Protractor, ruler Interaction (30 minutes) Activity A: Investigate Me! Procedures • What is the relationship between the sides of a triangle and the angles opposite them? • Write the Triangle Inequality Theorem in if-then form. Making Conjecture • 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 𝐴𝐶̅̅̅̅ and 𝐵𝐶̅̅̅? in 𝐷𝐹̅̅̅̅ and 𝐸𝐹̅̅̅̅? • What is the sum of the interior angles of ∆ABC? ∆DEF? • If ∠B ≅ ∠E, and ∠C ≅ ∠F, what additional information is required to tell that the triangles are congruent using SAS Congruence? • If 𝐴𝐶̅̅̅̅ ≅ 𝐷𝐹̅̅̅̅ and ̅𝐵𝐶̅̅̅ ≅ 𝐸𝐹̅̅̅̅, what additional information is required to tell that the triangles are congruent using SSS Congruence? Activity B: Materials Needed

10. 2 3 5 1 4 Angle-Side Relationship Theorem • If two sides are congruent and the third side of the first triangle is longer, then the included angle is larger. Discussion • The sum of the lengths of any two sides is greater than the length of the remaining side. Converse of Hinge Theorem or SSS Inequality Theorem Triangle Inequality Theorem • An exterior angle is greater than either remote interior angle. • Larger angle opposite larger side; larger side opposite larger angle. Hinge Theorem or SAS Inequality Exterior Angle Inequality Theorem • If two sides of one triangle are congruent to two sides of another triangle, the third side of the first triangle is longer if the included angle is greater.

11. 3. Integration Application: Engineering and 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

13. 4. Assessment

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

15. Thank You