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 4 3 2 5 7 8 6

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

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

Which of these shapes are congruent to the yellow one? 4 1 2 3 8 6 5 9 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? YZ Y B X A Z C

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

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

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 4 3 2 5 7 8 6

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

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

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

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

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.

Congruent and Similar Figures 9.7 Notes Congruent and Similar Figures Congruent: same size and shape have congruent corresponding angles and sides Similar: same shape, but different size have congruent angles, but MUST use proportions to find the side lengths