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Congruent figures are the same shape AND size. A: The same shape, but different sizes? B: Different shapes, but the same size? Are these figures: •Congruent •Similar but not congruent •Neither The figures are similar because they are the same shape, but not the same size. 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. 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 Original Copy Original Copy Exact Copy Enlargement Reduction Copy machine set to 100% Copy machine is set to 200% Copy machine is set to 50% Size-change factor1X is Size-change factor2X is Size-change factor1isx 2 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 1.5 cm ? cm A 3 cm O C 3 cm 6 cm D Each side and its enlargement form a pair of sides called corresponding sides. (1) Corresponding side of TC --> GD (2) Corresponding side of CA--> DO (3) Corresponding side of TA--> GO Length of corresponding sides GD=3 TC=1.5 DO=6 CA=3 GO=? TA=2 Ratio of Lengths 3/1.5=2 6/3=2 ?/2=2 The size-change factor is 2x. G ? cm T 2 cm 3 cm 1.5 cm O A C 3 cm D 6 cm (1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle. (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 Not change angle Different size Same shape Similar polygons Corresponding side Size-change factor Two angles whose measure add up to 90°. 45° 45° Example 1: Quadrangles ABCD and EFGH are similar. How long is side AD? How long is side GH? (1) What is size-change factor? 12÷ 4= 3 & 18÷ 6=3 (2) What is corresponding side EH of AD ? (3) How long is side AD? AD = 5 H 15 cm E ?cm ? cm D 12cm (4) What is corresponding side CD of GH? (5) How long is side GH? 7 x 3 = GH, GH = 21 A 7cm 4cm B C 6cm F 18 cm G Two angles whose measures add up to 180°. 90° 90° When a transversal intersects two parallel lines, eight angles are formed. 1. 2 3. . 4. 5. 7. 6. 8. 1. 2 3. . 4. 5. 6. 7. 8. Angle 3 and Angle 6 are congruent angles. This means they have the same measure. 1. 2 3. . 4. 5. 6. 7. 8. Angle 4 and Angle 5 are congruent angles. 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. Alternate Interior Angles are on “alternate” sides and on the “interior” of the parallel lines. 1. 2 3. . 4. 5. 6. 7. 8. Angle 1 and Angle 4 are congruent angles. 1. 2 3. . 4. 5. 6. 7. 8. Angle 2 and Angle 3 are congruent angles. 1. 2 3. . 4. 5. 6. 7. 8. Angle 5 and Angle 8 are congruent angles. 1. 2 3. . 4. 5. 6. 7. 8. Angle 6 and Angle 7 are congruent angles. 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. Vertical Angles are diagonally across from each other. These angles are a bit trickier. You have to imagine cutting your diagram apart, and then pasting one part on top of the other. 1. 2 3. . 4. 5. 6. 7. 8. Angle 1 and Angle 5 are congruent angels. 1. 2 3. . 4. 5. 6. 7. 8. Angle 2 and Angle 6 are congruent. 1. 2 3. . 4. 5. 6. 7. 8. Angle 3 and Angle 7 are congruent angles. 1. 2 3. . 4. 5. 6. 7. 8. Angle 4 and Angle 8 are congruent angles. 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. 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! Angle 2 measures 110°. What do the other angles measure? 1. 2 3. . 4. 5. 6. 7. 8.