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Do Now 4/25 If m∠1 = x + 5, m∠2 = 3(x + 4), and m∠4 = 3(x + 9) in the diagram below, find m∠4. Essential Question: What are the properties of similar figures?

Agenda Do Now Good Things Properties of Similar Triangles

Good Things!

Recap of yesterday What type of figures are formed by dilations – similar or congruent? What makes two figures congruent? Similar figures have the same shape but are different in size: true or false? What is a distortion? What is the formula for finding the scale factor? Scale factor greater than 1 – enlargement or reduction?

Notes: Similarity Similar triangles have the same shape, but may be different in size Just like with determining congruent figures, it is possible to determine similarity based on the angle measures and lengths of the sides of triangles

Similarity If two triangles are similar… corresponding angles are congruent measures of corresponding sides are proportional Proportional means to have a constant ratio This is why distortions aren’t similar! Are these ratios proportional? Cross multiply!

Proportion Practice A poster of the tallest buildings in the world hangs in a hallway. The scale on the poster is 0.5 inches = 45 feet. The height of the tallest building in the world, Burj Khalifa in Dubai, is about 30.25 inches on the poster. What is the actual height of Burj Khalifa?  Set up a proportional ratio!

Similarity If triangle ABC is similar to triangle DEF, the vertices of the two triangles correspond in the same order as they are named A corresponds to D B corresponds to E C corresponds to F Like with congruent triangles, corresponding angles and sides can be determined by the order of the letters How would we name these triangles?

Similar Triangles Angles are congruent Side lengths are proportional They all equal the same scale factor!!!

Similar Triangles 10 8 5 6 4 3 What is the scale factor of dilation? 2. Are the triangles similar?

Similar Triangles Side- Side- Side Similarity Statement If all the sides of two figures are proportional, you can prove that the figures are similar Are triangles EDF and BAC similar?

Angle-Angle Criterion We can NEVER use just angles to prove congruence We CAN use angles to prove similarity Angle Angle Criterion If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Angle-Angle Criterion Are the triangles similar? What is the length of side DF?

Similar Triangles If all of the ratios of the SIDE LENGTHS are proportional, they are similar! AB/DF BC/FE AC/DE First, you need to find the side lengths

Group Practice 1. Are these triangles similar? Why or why not? 2. Name the triangles to show similarity (order matters!)

Group Practice Find the missing angle measures (remember, angles in similar triangles are congruent!) <C, <D, & <E Find the missing side lengths

Group Practice First, prove that they are similar Next, set up a proportion to find side EF

Similar Triangles Recap 1. Determine if they meet the AA Criterion (find 2 congruent angles) OR the SSS similarity statement (all sides are proportional) 2. Set up proportions to solve for the missing sides

Practice Problems File on class website Solution station at the front