WARM - UP What two properties must be true in order to show that two shapes are similar? The exchange rate of the Mexican Peso to American dollars is to 1. If you paid 189 pesos for shirt roughly how many dollars did you spend? The Wright brothers made the world’s first flight in a power- driven airplane. The flight lasted for 12 seconds at an average speed of 10 feet per second. The ratio of the airplane’s wingspan to distance flown was 1:3. How long was the wingspan?

8.4 SIMILAR TRIANGLES

LEARNING OUTCOMES I will be able to prove that triangles are similar by identifying and/or showing that the properties of similarity exist. I will be able to prove that triangles are similar by using AA Similarity Theorem.

SIMILAR TRIANGLES How many angles of a triangle do you need to determine whether they are similar?

ACTIVITY 1.) Using cardstock create a 90 angle and a 45 angle. 2.) Using the angles you created construct a triangle using a piece of scratch paper. 3.) Give your triangle a name and correctly label the angles. 4.) Find the measurements of the sides of your triangle and write them down into your notes. 5.) Wait for further instructions.

ACTIVITY 6.) Switch seats with someone else in the class and create a statement of proportionality. 7.) Measure the sides of their triangle and compare the ratios. 8.) Are your triangles similar? 9.) Repeat steps 6-8.

ANGLE ANGLE SIMILARITY If you know two angles are congruent in a triangle then the triangles are similar.

TRY THIS ON YOUR OWN

HOW DO WE USE SIMILAR TRIANGLES? 1.) Physics and science 2.) Approximate heights or distances 3.) Games and sports, like pool.

MINI GOLF ACTIVITY In your group each person must design a hole of golf that uses similar triangles. If you can try and make it so your course has different levels of difficulty. Once you are finished you will trade with another group and attempt to complete their golf course.

WHAT ABOUT FOR OTHER SHAPES? Does Angle-Angle Simlarity work for other polygons?

PROVE THE PYTHAGOREAN THEOREM Hint: Use similar triangles. A B C D

HOMEWORK Pg. 483: 9, 12—26, QUIZ NEXT CLASS!