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Congruent triangles Congruent triangles are triangles that have the same size and shape. Congruent triangles are triangles that have the same size and shape. Congruent triangles Similar triangles are triangles that have the same size and shape. Congruent triangles Similar triangles are triangles that have the same size and shape. Congruent triangles Similar triangles have the same shape but different sizes. Congruent ? Similar ? How do we know when triangles are similar? How do we know when triangles are similar? 2 5 4 1 2.5 2 How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 These are congruent How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 These are congruent How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 These are congruent Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. (Proportional means they have to divide to the same thing.) 2 5 4 1 2.5 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 4 ÷ 2 = 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 4 ÷ 2 = 2 2 ÷ 1 = 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 4 ÷ 2 = 2 2 ÷ 1 = 2 5 ÷ 2.5 = 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 4 ÷ 2 = 2 2 ÷ 1 = 2 5 ÷ 2.5 = 2 Their corresponding sides have to be proportional. How do we know when triangles are similar? Their corresponding angles have to be congruent. 2 5 4 1 2.5 2 4 ÷ 2 = 2 2 ÷ 1 = 2 5 ÷ 2.5 = 2 All the same For shapes to be similar their corresponding angles must be their corresponding sides must be proportional ? congruent ? We can use similarity We can use similarity to find unknown sides We can use similarity to find unknown sides 2 5 x 10 We can use similarity to find unknown sides 2 5 x 10 corresponding sides These are We can use similarity to find unknown sides 2 5 x 10 corresponding sides These are We can use similarity to find unknown sides 2 5 x 10 2 x = 10 5 We can use similarity to find unknown sides 2 5 x 10 Solve 2 x = 10 5 We can use similarity to find unknown sides 2 5 x 10 Solve 2 x 5x = 20 = 10 5 We can use similarity to find unknown sides 2 5 x 10 Solve 2 x 5x = 20 x = 4 = 10 5 x x = 5 8 10 There are three ways to prove trangles similar There are three ways to prove trangles similar AA There are three ways to prove trangles similar sAs AA There are three ways to prove trangles similar sAs sss AA For AA you have to have two sets of angles congruent For AA you have to have two sets of angles congruent These are congruent For AA you have to have two sets of angles congruent These are congruent and these are too For sAs one set of angles needs to be congruent 10 6 5 3 For sAs one set of angles needs to be congruent These are congruent 10 6 5 3 For sAs one set of angles needs to be congruent and the sides making up that angle must 10 6 5 3 proportional For sAs one set of angles needs to be congruent and the sides making up that angle must 10 6 5 3 10∕5 = 2 proportional For sAs one set of angles needs to be congruent and the sides making up that angle must 10 6 5 3 10∕5 = 2 6/3 = 2 proportional For sAs one set of angles needs to be congruent and the sides making up that angle must 10 6 5 3 10∕5 = 2 6/3 = 2 proportional sAs AA Side Angle Side ? Angle Angle ? For sss all the side need to be proportional For sss all the side need to be proportional 10 4 8 5 2 4 For sss all the side need to be proportional 10 4 8 5 2 4 10/5 = 2 For sss all the side need to be proportional 10 4 8 5 2 4 10/5 = 2 8/4 = 2 For sss all the side need to be proportional 10 4 8 5 2 4 10/5 = 2 8/4 = 2 4/2 = 2 9 3 sss ? 4 6 1 3 1 sAs ? 2 AA ? 12 3 |