Polygon Angle-Sum Theorems - Envision Algebra 1 PDF

Presented by: MR. MIKE DANEL JESSIE A. SEDORIPA  CLASSROOM RULES 1. Ask Questions Freely: Curiosity is encouraged—no question is too small. 2. Collaborate Actively: Work together, share ideas, and learn from one another. 3. Speak Up and Share: Your voice matters; contribute your t...

Presented by: MR. MIKE DANEL JESSIE A. SEDORIPA  CLASSROOM RULES 1. Ask Questions Freely: Curiosity is encouraged—no question is too small. 2. Collaborate Actively: Work together, share ideas, and learn from one another. 3. Speak Up and Share: Your voice matters; contribute your thoughts regularly. 4. Stay Open-Minded: Respect different opinions and be ready to explore new ideas. 5. Have Fun While Learning: Enjoy the process, and bring your energy and creativity!  Presented by: MR. MIKE DANEL JESSIE A. SEDORIPA The Polygon Angle-Sum Theorems Second Term: Week 5 Envision Algebra 1 pp. 245 - 251 objectiveS 1. Show that the sum of the exterior angles of a polygon is 360°and use that to solve problems. 2. Show that the sum of the interior angles of a polygon is the product of 180° and 2 less than the number of sides, and use that to solve problems. REVIEW OF THE PAST LESSON  vocabulary BUILDER EXTERIOR ANGLE EXERORI GANEL is an angle formed between one side of a polygon and the extension of an adjacent side. It is located outside the polygon. In a polygon, this angle is supplementary to the adjacent interior angle, meaning the sum of the exterior and interior angles at each vertex equals 180°.  vocabulary BUILDER INTERIOR GANEL NITERORI ANGLE is an angle formed between two adjacent sides of a polygon, located inside the polygon. In a convex polygon, these angles are the angles between the sides at each vertex. The sum of the interior angles of a polygon depends on the number of sides, and for an n-sided polygon, the sum of the interior angles is given by the formula: Sum of interior angles = (n−2) × 180∘ EXPLORE POLYGON INTERIOR ANGLE SUMS EXPLORE POLYGON INTERIOR ANGLE SUMS Use and Connect Math Can any of the vertices be chosen as the vertex from which to draw the diagonals? Would the number of triangles change? Answer: Yes, the number of triangles will not change since you cannot draw a diagonal to the two adjacent vertices. You will always make n - 2 triangles. EXPLORE POLYGON INTERIOR ANGLE SUMS 1. 6 triangles 2. 1,080° EXPLORE POLYGON INTERIOR ANGLE SUMS THINK ABOUT THIS! How do you find the missing angle of the pentagon? Answer: Calculate the sum of the interior angles for a pentagon. Then subtract the known angles to find the missing angle. APPLY THE POLYGON INTERIOR ANGLE-SUM THEOREM APPLY THE POLYGON INTERIOR ANGLE-SUM THEOREM  APPLY THE POLYGON INTERIOR ANGLE-SUM THEOREM Pose Purposeful Question How is the Polygon Interior Angle- Sum Theorem used? UNDERSTAND EXTERIOR ANGLE MEASURES OF A POLYGON UNDERSTAND EXTERIOR ANGLE MEASURES OF A POLYGON  UNDERSTAND EXTERIOR ANGLE MEASURES OF A POLYGON THINK ABOUT THIS! Does the number of sides matter when finding the sum of exterior angles? What is the sum of the measures of the exterior angles of any convex polygon? UNDERSTAND EXTERIOR ANGLE MEASURES OF A POLYGON 3. 360° FIND AN EXTERIOR ANGLE MEASURE  v FIND AN EXTERIOR ANGLE MEASURE 4. 70  FIND AN EXTERIOR ANGLE MEASURE USE AND CONNECT MATH What does the left side of the first equation iin Step 1 represent? What is the left side set equal to 360? INDIVIDUAL ACTIVITY INDIVIDUAL ACTIVITY  ASSESSMENT 3 Things I learned today 2 Things I found interesting 1 Question I still have How did you feel about today’s lesson?  Addressing your thoughts!  WE WORK TOGETHER, WE LEARN TOGETHER! Thank you for Listening!