Angles and Polygons - LPU Laguna High School PDF

ANGLES AND POLYGONS FIRST QUARTER │ LESSON 1 LEARN DIFFERENT. LIVE DIFFERENT.  Learning TARGETS At the end of this lesson, I can define regular and irregular polygons and determine the characteristics of polygons. I can utilize a ruler and protractor to meas...

ANGLES AND POLYGONS FIRST QUARTER │ LESSON 1 LEARN DIFFERENT. LIVE DIFFERENT.  Learning TARGETS At the end of this lesson, I can define regular and irregular polygons and determine the characteristics of polygons. I can utilize a ruler and protractor to measure sides and angles accurately for constructing regular and irregular polygons. I can describe triangles, quadrilaterals, and regular polygons with given angle measures.  LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. earn it L about No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  ANGLES AND POLYGONS Constructing Regular and Irregular Polygons LEARN DIFFERENT. LIVE DIFFERENT. LPU LAGUNA HIGH SCHOOL DEFINITION LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. POLYGONS closed two-dimensional shapes made up of line segments. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. The following are the different parts of the polygon. ○ The side refers to the line segments that enclose the polygon. ○ The vertex (plural: vertices) refers to the point of intersection of the sides of a polygon. ○ The angle refers to the opening that the two sides form. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. Examples of Polygons No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. The following figures are not polygons. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL DEFINITION LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. REGULAR POLYGONS polygons that have all sides of equal length and all angles Of equal measure No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL EXAMPLE LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. The figure below is an example of a regular polygon. The tick marks indicate that its sides have the same length, and its angles have equal measures. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL EXAMPLE 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. A plane figure with five sides that all measure 3 cm each and five angles all measuring 108° each. Is the given figure a regular polygon? No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL EXAMPLE 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. A plane figure with five sides that all measure 3 cm each and five angles all measuring 108° each. Is the given figure a regular polygon? Step 1: Determine if the figure is a polygon. Step 2: Determine if the polygon is a regular polygon. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL try it yourself! LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Construct an equilateral triangle. An equilateral triangle has three sides with equal measures. Each angle measures 60°. Step 1: Draw a line of any length. Step 2: At one end of the line, use a protractor to measure an angle of 60°. Draw the next line from that point and at the given angle. Make sure that the new line has the same length as the previous line. Step 3: Repeat Step 2 until you complete the triangle. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL SEATWORK 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. I. Write P on the line provided if the figure is a polygon and NP if it is not. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL SEATWORK 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. II. Write R on the line provided if the polygon is regular and IR if it is irregular. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL SEATWORK 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. I. Write P on the line provided if the figure is a polygon and NP if it is not. NP P P P NP No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL SEATWORK 1 LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. II. Write R on the line provided if the polygon is regular and IR if it is irregular. R R IR IR IR No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  ANGLESTypes AND POLYGONS of Polygons LEARN DIFFERENT. LIVE DIFFERENT.  Learning TARGETS At the end of this lesson, I can classify polygons based on the number of sides they have. I can differentiate regular and irregular polygons. I can differentiate convex and non-convex polygons. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. TYPES OF POLYGONS No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of Polygons No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. What is a Triangle? No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL DEFINITION LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Triangle a three-sided two-dimensional figure whose interior angles are equal to 180°. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Properties of a Triangle The sum of the interior angles of a triangle is 180 degrees When two sides of a triangle are added, it is always greater than the third side Similarly, if the two sides of a triangle are subtracted, it is always less than the third side Two triangles are said to be similar if the corresponding angles are congruent and the corresponding side lengths are proportional No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of Triangle No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Triangle Based on Sides No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Triangle Based on Angles No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. What is a Quadrilaterals? No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL DEFINITION LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Quadrilaterals closed shape polygon that has four sides, four vertices and four angles. The sum of interior angles of quadrilaterals is always equal to 360 degrees. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Properties of a Quadrilaterals 4 vertices and 4 sides enclosing 4 angles The sum of all interior angles of a quadrilateral is 360 degrees We can also derive the sum of interior angle from the formula of polygon i.e. (n -2) × 180, where n is equal to the number of sides of the polygon No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Quadrilaterals No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Quadrilaterals No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Quadrilaterals No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons Pentagon has 5 sides and 5 vertices has 5 diagonals sum of the interior angles is 540 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. b ta in to o f w Ho umber o th e n s ? ona l dia g No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Diagonal of a Polygon Formula n ( n - ________3 ) 2 No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons HEXAGON has 6 sides and 6 vertices has 9 diagonals sum of the interior angles is 720 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons HEPTAGON has 7 sides and 7 vertices has 14 diagonals sum of the interior angles is 720 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons OCTAGON has 8 sides and 8 vertices has 20 diagonals sum of the interior angles is 1080 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons NONAGON has 9 sides and 9 vertices has 27 diagonals sum of the interior angles is 1260 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Types of a Polygons Decagon has 10 sides and 10 vertices has 35 diagonals sum of the interior angles is 1440 degrees No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. s an d ha pe r d o s c t o u How i m p a gle s an liv es ? No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. ag in e o u im o Ca n y it h n o rld w a w p e s ? sh a No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. earn it L about No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  ANGLES AND POLYGONS Convex and Concave Polygons LEARN DIFFERENT. LIVE DIFFERENT.  Learning TARGETS At the end of this lesson, I can classify polygons based on the number of sides they have. I can differentiate regular and irregular polygons. I can differentiate convex and non-convex polygons.  LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. yg on ol z le P puz No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL INSTRUCTIONS LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. 1.Each group will have its own set of tangram pieces. 2.Complete the tangram puzzle to form a polygon. All of the pieces must be utilized. 3. The first group to finish the puzzle will earn additional points. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL INSTRUCTIONS LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  ANGLES AND POLYGONS Convex and Concave Polygons LEARN DIFFERENT. LIVE DIFFERENT.  LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. Convex Polygon A polygon that has all angles pointed outward. The measures of the interior angles in a convex polygon are strictly less than 180 degrees. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.  LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. Properties of a Convex Polygon All interior angles measure less than 180°. All diagonals line in the interior of the polygon. If the sides of the polygon are extended, the lines will not intersect in the interior of the polygon. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LET’S DIFFERENTIATE LPU LAGUNA HIGH SCHOOL LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L E A R N D I F F E R E N T. L I V E D I F F E R E N T. L I V E D I F F E R E N T. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. Concave Polygon A polygon has at least one angle that measures more than 180 degrees. The vertices (endpoints) of this polygon are inwards as well as outwards. No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L. LPU LAGUNA HIGH SCHOOL L E A R N D I F F E R E N T. L I V E D I F F E R E N T. a ny ons? e st i qu No part of this material may be copied of reproduced in whatever form without the express written permission of LPU-L.