Similar Triangles Section 7.4 Curriculum Outcome: Demonstrate an Understanding of Similar Polygons

Properties of Similar Triangles D To identify that ∆ABC and ∆DEF are similar, we only need to know that: <A=<D and <B=<E and <C=<F; or AB~ DE and BC~ EF and AC~ DF A B C E F

Properties of Similar Triangles D So because of this ∆ABC and ∆DEF are similar. A B C E F

Properties of Similar Triangles Let’s try this with triangles off a grid…Similar or not? K 30o J B 90o 30o C 60o 60o 90o A L

Properties of Similar Triangles Regardless of orientation, the corresponding angles are equal, so ∆ABC~∆JKL. K 30o J B 90o 30o C 60o 60o 90o A L

Properties of Similar Triangles J What about these two triangles? O × X Y O × G P

Properties of Similar Triangles J J 2 2 O × X Y 5 What if we wanted to determine side GP? How could we use our knowledge of similar triangles? 4 O × G P

Properties of Similar Triangles J J 2 2 O × X Y 5 4 Now we can use corresponding sides to determine our missing side: GP. O × G P

Properties of Similar Triangles J J 2 2 6 O × X Y 5 4 O × G P

Properties of Similar Triangles J J 2 6 O × X Y 5 O × G P

Properties of Similar Triangles 6 4 2.5 7.5 5 5 4 6 6 !!!APPLAUSE!!!

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T So now what? What are the corresponding sides? What are the corresponding angles? 6 R

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T 6 R

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T 6 R

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T 6 R

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T 6 R

Properties of Similar Triangles U 6 4 S 7.5 Q 5 T 6 R

Assignment Time Pg. 348-351 #3,4,5,6, 7, 8, 9,12,13,15