1. 4/25

2. 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?

3. Agenda
Do Now
Good Things
Properties of Similar Triangles

4. Good Things!

5. 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?

6. 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

7. 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!

8. 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 inches on the poster. What is the actual height of Burj Khalifa? 
Set up a proportional ratio!

9. 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?

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

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

12. 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?

13. 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.

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

15. 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

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

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

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

19. 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

20. Practice Problems
File on class website
Solution station at the front