Congruent and Similar Shapes 6 1 2 2

Congruent and Similar Shapes 6. 1. 2. 2 Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts

I can… • • Identify congruent and similar figures Find missing sides and angles of congruent and similar figures Self Assessment 5 - I can do it without help & teach others. 4 - I can do this with no help, but I don’t know if I can explain it. 3 - I can do this with a little help. 2 - I can do this with a lot of help! 1 - I don’t have a clue.

What makes a pair of shapes “congruent”? Same angles Same side lengths Can be rotated or a mirror image A cut-out of one shape will always fit exactly over the other

Which of these shapes are congruent to the yellow one? 1 3 4 2 6 7 8 5

Which of these shapes are congruent to the yellow one? 1 3 4 2 6 7 8 5

Which of these shapes are congruent to the yellow one? 1 4 3 2 8 6 5 7 9

Which of these shapes are congruent to the yellow one? 1 3 2 6 5 7

Using Corresponding Part When 2 figures are congruent the corresponding parts are congruent. (angles and sides) If Δ ABC is to Δ XYZ, which side is to BC? Y B A C X Z YZ

Using Corresponding Part If Δ ABC is to Δ XYZ, which side is to AB? Y B A C X Z XY

Using Corresponding Part If Δ ABC is to Δ XYZ, which angle is to angle Z? Y B A C X C Z

What makes a pair of shapes “similar”? Same angles Sides in the same proportion Can be rotated or reflected One is an enlargement of the other Scale factor gives degree of enlargement: – – – Scale factor 2 → size is doubled Scale factor ½ → size is divided by 2 Scale factor 1 → size doesn’t change → congruent too

Which of these shapes are similar to the yellow one? 1 3 4 2 6 7 8 5

Which of these shapes are similar to the yellow one? 1 3 4 2 6 7 8 5

Using similarity Since shapes are similar, their sides are in the same proportion 6 = a 9 12 9 cm 12 • 6 = 9 a 6 cm 72 = 9 a 9= 9 8= a 12 cm a

These figures are similar. Find the values of x. 3 = 4 6 x 4 • 6 = 3 x 24 = 3 x 3 = 3 8= x y x

These figures are similar. Find the values of y. y 50 o 8 cm

I can… • • Identify congruent and similar figures Find missing sides and angles of congruent and similar figures Self Assessment 5 - I can do it without help & teach others. 4 - I can do this with no help, but I don’t know if I can explain it. 3 - I can do this with a little help. 2 - I can do this with a lot of help! 1 - I don’t have a clue.

9. 7 Notes Congruent and Similar Figures v Congruent: same size and shape § have congruent corresponding angles and sides v Similar: same shape, but different size § have congruent angles, but MUST use proportions to find the side lengths