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Introduction to Polygons: Types, Congruency, and Similarity

Explore the world of polygons and learn about their types, congruency, and similarity. Find examples and understand the concept of corresponding sides and the scale factor. Engaging and informative presentation!

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Introduction to Polygons: Types, Congruency, and Similarity

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  1. Welcome to the Wonderful World of Polygons

  2. What We Hope You Learn by the End of this Presentation: • What is a polygon? • What are the different types of polygons? • What is a congruent polygon? • What is a similar polygon? • What are some examples of these polygons?

  3. What Is a Polygon? A polygon is a plane having three or more sides. Types of Polygons: Convex polygon: all the sides are pushed outward. Concave polygon: at least two sides are pushed inward. Regular polygon: all the sides have the same length and their angles are all the same size.

  4. Let's Play a Polygon Matching Game: Take a minute to match the name up with the figure . . . pentagon triangle octagon quadrilateral hexagon heptagon

  5. What are Congruent Polygons? Congruent polygons are polygons that have the same size and the same shape. fact: Congruent shapes have all their sides and angles congruent. fact:

  6. Let's See Some Congruent Polygons: Notice how the second figures have the same shape and size of the first – they match exactly. Now we are going to take a look at similar polygons . . .

  7. What are Similar Polygons? Let's find some examples outdoors.

  8. Can you find the similar matches? Now, Let's Think about Similar in Mathematics!!

  9. Can you find similar polygons? Same shape (1) Triangle (2) Rectangle Different size (3) Pentagon Angle does not change (4) Hexagon Reduction (5) Octagon Enlargement

  10. Definition: Now, let’s define similar !! Figures that have exactly same shape are called similar figures. Properties: (1) In polygons, the size of angles does not change. (2) One figure is an enlargement or reduction of the other. (3) Congruent figures are similar because they gave the same shape.

  11. How can we know the length of sides in similar figures? If two figures are similar, one figure is an enlargement of the other. The size-change factor tells the amount of enlargement or reduction. Example 1: If a copy machine is used to copy a drawing or picture, the copy will be similar to the original. Original Copy Exact Copy Copy machine set to 100% Size-change factor is Original Copy Enlargement Copy machine is set to 200% Size-change factor is Original Copy Reduction Copy machine is set to 50% Size-change factor is 1X 2X

  12. Example 2: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO? T G 2 cm ? cm 1.5 cm A 3 cm O 3 cm C 6 cm D Each side and its enlargement form a pair of sides called corresponding sides. GD (1) Corresponding side of TC --> DO (2) Corresponding side of CA--> The size-change factor is 2x. (3) Corresponding side of TA--> GO

  13. (1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle. G ? cm T 2 cm 3 cm O 1.5 cm A 6 cm 3 cm C D (2) Now, let’s find the length of side GO i) What side is corresponding side of GO? TA ii) What is the size-change factor? 2X iii) Therefore, GO= size-change factor x TA iv) So, GO= 2 x 2 = 4 cm

  14. What we just learned about similar polygons ? Not change angle Different size Same shape Similar polygons Corresponding side Size-change factor

  15. Now, you try... Example 1: Quadrangles ABCD and EFGH are similar. How long is side AD? How long is side GH? 12÷4= 3 & 18÷6=3 What is size-change factor? What is corresponding side of AD ? How long is side AD? What is corresponding side of GH? How long is side GH? EH AD = 5 CD 7 x 3 = GH, GH = 21

  16. Let's Go Over What We Just Learned: What is a polygon? A polygon is a plane having three or more sides. What are congruent polygons? congruent congruent Congruent polygons are polygons that have the same size and the same shape. What are similar polygons? similar similar Similar polygons are polygons that have the same shape.

  17. Similar Polygons Circle Limit III M.C. Escher

  18. Similar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship.

  19. Just like congruent polygons, the corresponding angles in similar polygons must be congruent.

  20. A = 80° B = 30° Z = 170° W = ___ X = ___ D = ___ 80° 170° 30° B A W X Z Y D C

  21. The sides are a little different. They must be PROPORTIONAL. AB = BC = CD = DA WX XYYZ ZW B A W X Z Y D C

  22. This means I should be able to multiply each side of the smaller polygon by the same number and get it’s corresponding side on the bigger polygon. 4x2 = 8 4 3x2 = 6 5x2 = 10 3 5 2 2x2 = 4

  23. The SCALE FACTOR is the ratio of the corresponding sides or SMALLBIG BIG SMALL

  24. What is the scale factor of these polygons? 10 4 6 X 7 Z Y 8 10 4 5 2 = Scale Factor =

  25. 10 4 5 2 56 2 Z = = Use the scale factor to find the other sides 10 4 7 Z 6 X SF = Y 8 5X 2 7 58 2 Y = = 5y = 16 y = 16 = 3.2 5 5z = 12 z = 12 = 2.4 5 2x = 35 x = 35 = 17.5 2

  26. The End!

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