MATH EDUC 206 POLYGONS (ANGLE THEOREM.pptx

Powerpoint presentation about Polygons

1. POLYGONS Angle Theorems Prepared by: Joshua A. Angub, LPT MATH EDUC 206: Plane and Solid Geometry

2. At the end of the lesson, the students are expected to: Apply angle theorems to solve geometric problems. Construct polygons using GeoGebra Learning Objectives

3. ANGLE THEOREMS

4. Interior Angle of Polygons

5. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg

6. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg

7. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg

8. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg

9. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg

10. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg The General Rule: Each time we add a side (triangle to quadrilateral, then to pentagon, and so on), we add another to the total.     The Sum of Interior Angle   Each Angle (of Regular Polygon)  

11. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg Example 1: So, this is a decagon with 10 sides.           Therefore, the sum of the interior angle of a decagon is 1440.

12. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg Example 1: Since decagon is a regular polygon, we can find the measurement of each interior angle.     Therefore, each angle measures .          

13. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg Example 2: So, this is a dodecagon with 12 sides.           Therefore, the sum of the interior angle of a decagon is 1800.

14. Interior Angle of Polygons Reference: https://www.mathsisfun.com/geometry/images/interior-exterior-angles.svg Example 2: Since decagon is a regular polygon, we can find the measurement of each interior angle.     Therefore, each angle measures .          

15. Constants are numbers that have fixed values. Variables are symbols or letters that may take one or more value. Literal Coefficient is the variable including its exponent Numerical Coefficient the numerical factor of a term Algebraic Expressions The result of combining symbols such as letters, numbers, punctuations and operations of arithmetic. Base Is the factor which is to be multiplied by itself n times to obtain the product Exponent Tells us how many times the base is multiplied by itself.

16. 3 y + 2 Constant Variable

17. 5 a 2 Numerical Coefficient Literal Coefficient

18. 3 y + 2 Constant Variable Numerical Coefficient

19. Direction: Determine the constant/s and variable/s in each algebraic expression. Algebraic Variable/s Constant/s Expressions 1. b + 12 _________ _________ 2. 3 – m _________ _________ 3. n + 8 _________ _________ 4. 6p _________ _________ 5. 5m 3 +10n 2 +4 _________ _________

20. Fix me, I’m broken

21. Direction: Construct an algebraic expressions. The groups are free to construct four algebraic expressions. Then, the group will identify the constants and variables, literal coefficients and numerical coefficients based on what algebraic expression you have constructed.

22. A. Direction: Match each term in column A with the correct meaning in column B by writing the letter in the space provided that corresponds to each item. A B ___1. Sequence Sum of the terms in the sequence ___2. Series b . The sum of the terms in an arithmetic sequence ___3. Arithmetic Sequence c. Constant difference between consecutive terms on an arithmetic sequence ___4. Arithmetic Series d. Ordered list of numbers that follows a specific pattern. ___5. Common Difference e. Ordered set of numbers that have a common difference between each consecutive terms

23. A. Direction: Match each term in column A with the correct meaning in column B by writing the letter in the space provided that corresponds to each item. A B ___1. Polynomials The numerical factor in a term ___2. Constants b . It is a special algebraic expression that represents a sum of one or more terms containing nonnegative whole numbers exponents on the variables. ___3. Variables c. the variable including its exponent ___4. Numerical Coefficient d. A symbol or letters which represents any number from a given replacement set ___5. Literal Coefficient e. A term with no variabl e or a term with fixed value

24. B. Complete the table. Write your answers to the corresponding column.       Coefficients Variable/s Constant/s Numerical Literal 1. 2. 3. 4. 5.       Coefficients Variable/s Constant/s Numerical Literal

25. C. Tell whether the given expression is a polynomial or not . Write P if the expression is polynomial and NP if not polynomial.

26. Algebraic Expression Terms Number of Terms Degree of the Term 1 st Term 2 nd Term 3 rd Term 1.           2.           3.           4.           5.           Algebraic Expression Terms Number of Terms Degree of the Term 1 st Term 2 nd Term 3 rd Term                                                   D. Complete the table. Write your answers to the corresponding column.

27. B. Complete the table. Write your answers to the corresponding column.       Coefficients Variable/s Constant/s Numerical Literal 1. 4x 2 -8 x -8 4 x 2 2. 25r 4 +2 r 2 25 r 4 3. –a+4 a 4 -1 a 4. 10m 2 -7mn+1 m, n 1 10, 7 m 2 , mn 5. 2 r 2       Coefficients Variable/s Constant/s Numerical Literal 1. 4x 2 -8 x -8 4 x 2 2. 25r 4 +2 r 2 25 r 4 3. –a+4 a 4 -1 a 4. 10m 2 -7mn+1 m, n 1 10, 7 m 2 , mn r 2

28. Criteria Accuracy 15 Cooperation 10 Discipline 5 Total 30