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Grade 7 3.02 Similar and Congruent polygons

Grade 7 3.02 Similar and Congruent polygons. Congruent figures are the same shape, but can be different sizes?. TRUE OR FALSE?. Congruent figures are the same shape AND size. FALSE!!!!!!. If two figures are similar, are they. A: The same shape, but different sizes?

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Grade 7 3.02 Similar and Congruent polygons

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  1. Grade 7 3.02 Similar and Congruent polygons

  2. Congruent figures are the same shape, but can be different sizes? TRUE OR FALSE?

  3. Congruent figures are the same shape AND size. FALSE!!!!!!

  4. If two figures are similar, are they A: The same shape, but different sizes? B: Different shapes, but the same size?

  5. A: The same shape, but not necessarily the same size.Similar figures have to be the same shape, however, they can be the same or different sizes.

  6. Are these figures: • Congruent • Similar but not congruent • Neither

  7. The figures are similar because they are the same shape, but not the same size.

  8. Now, let’s define similar !! Definition: 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.

  9. 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

  10. 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

  11. G ? cm T 2 cm 3 cm O 1.5 cm A (1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle. 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

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

  13. Complementary Angle Two angles whose measure add up to 90°. 45° 45°

  14. 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

  15. Supplementary Angles Two angles whose measures add up to 180°. 90° 90°

  16. Congruent Angles When a transversal intersects two parallel lines, eight angles are formed.

  17. 1. 2. 3. 4. 5. 6. 7. 8.

  18. Alternate Interior Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 3 and Angle 6 are congruent angles. This means they have the same measure.

  19. Alternate Interior Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 4 and Angle 5 are congruent angles.

  20. RECAP SO.... The measure of angle 4 and the measure of angle 6 are congruent AND The measure of angle 3 and the measure of angle 5 are congruent.

  21. NOTE Alternate Interior Angles are on “alternate” sides and on the “interior” of the parallel lines.

  22. Vertical Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 1 and Angle 4 are congruent angles.

  23. Vertical Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 2 and Angle 3 are congruent angles.

  24. Vertical Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 5 and Angle 8 are congruent angles.

  25. Vertical Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 6 and Angle 7 are congruent angles.

  26. RECAP The measures of Angle 1 and Angle 3 are congruent. The measures of Angle 2 and Angle 4 are congruent. The measures of Angle 5 and Angle 7 are congruent. The measures of Angle 6 and Angle 8 are congruent.

  27. NOTE Vertical Angles are diagonally across from each other.

  28. Corresponding Angles These angles are a bit trickier. You have to imagine cutting your diagram apart, and then pasting one part on top of the other.

  29. Corresponding Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 1 and Angle 5 are congruent angels.

  30. Corresponding Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 2 and Angle 6 are congruent.

  31. Corresponding Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 3 and Angle 7 are congruent angles.

  32. Corresponding Angles 1. 2. 3. 4. 5. 6. 7. 8. Angle 4 and Angle 8 are congruent angles.

  33. RECAP Angle 1 and Angle 5 are congruent. Angle 2 and Angle 6 are congruent. Angle 3 and Angle 7 are congruent. Angle 4 and Angle 8 are congruent.

  34. Demonstrate Your Knowledge Now that you’ve seen what is congruent, you can take the measurement of “1” angle and figure out the others. Let’s try it!

  35. Angle 2 measures 110°. What do the other angles measure? 1. 2. 3. 4. 5. 6. 7. 8. WHY??

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