1. Dilations and Similarity Shortcuts
DO NOW 12/8:
Write an equation that will
show the tree’s height (h) in
terms of the shadow (s)
Dilations and Similarity Shortcuts
Agenda
Embedded Assessment Review
Triangles Cut by Parallel Lines
Dilations
Similarity Shortcuts: AA
Debrief

2. Triangles Cut by Parallel Lines
Would triangle SET still be similar to NEW if we “lowered” line ST to y=6?
How is this related to our discovery about triangle similarity shortcuts?
Triangle Proportionality Theorem (or Side-Splitter Theorem)
“If a line is parallel to one side
of a triangle and intersects the
other two sides of the triangle,
the line divides these two sides
proportionally.”
**MUST BE IN NOTES!**

3. Lesson 15: Review

4. Lesson 15: Exit Ticket When completed, turn it in for me to check.
If correct, congrats! You’re ready to move on to Lesson 16.
If incorrect, use corrections to continue practicing Lesson 15 with Problem Set #1-4 before moving on to Lesson 16.

5. Lesson 15: Debrief
Will ASA work as a similarity shortcut? Why? What about AAS?
Why are only two angles (AA) sufficient evidence to prove that two triangles are similar?

6. Ratio Method and Dilations
Take a ruler and a piece of graph paper.
Draw any triangle ABC (use the grid!)
Pick a point P not on your triangle, and draw a ray through each vertex.
Pick a scale factor. Increase or decrease lines AB, .
Is the resulting triangle similar? (You can verify using your ruler or the coordinate grid.)

7. Similarity and Right Triangle Ratios
DO NOW 12/9:
Are the two triangles similar?
If so, write the similarity statement.
Similarity and Right Triangle Ratios
Agenda
Ratio Method
Similarity Shortcuts (AA, ASA?, SSS, ASA?, SAS)
Right Triangle Ratios
Debrief

8. AA Similarity (Angle-Angle)
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.
Given:
and
**MUST BE IN NOTES!**
Conclusion:

9. SSS Similarity (Side-Side-Side)
If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 5 11 22 8 16 10
Given:
Conclusion:
**MUST BE IN NOTES!**

10. SAS Similarity (Side-Angle-Side)
If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar. 5 11 22 10
Given:
**MUST BE IN NOTES!**
Conclusion:

11. Between or Within Figure Comparisons
Between – each ratio made up of corresponding sides of two different triangles
Within – each ratios made up of two sides of one triangle

12. Right Triangle Ratios

13. Debrief: Right Triangles Similarity
What does it mean to use between-figure ratios of corresponding sides of similar triangles?
What does it mean to use within-figure ratios of corresponding sides of similar triangles?
How can within-figure ratios be used to find unknown side lengths of similar triangles?

14. Right Triangle Similarity
Learning Target
I can …indirectly solve for measurements involving right triangles using scale factors, ratios between similar
figures, and ratios within similar figures.
DO NOW 12/10:
Are the two triangles similar?
Right Triangle Similarity
Agenda
Note Card Similar Right Triangles
Special Right Triangle Ratios
Exit Ticket

15. Note Card: Similar Right Triangles
Draw diagonal AB on your note card.
Draw an altitude from one corner perpendicular to the diagonal.
Are the triangles similar? How can we know?

16. Creating Right Triangle Ratios

17. Exit Ticket

18. Special Similar Right Triangles
Learning Target
I can understand that the altitude of a right triangle (from the vertex of the right angle to the hypotenuse) divides the triangle into two similar right triangles that are also similar to the original right triangle.
DO NOW 12/11:
Find the measure of x.
Special Similar Right Triangles
Agenda
Complete Packets
Embedded Assessment
Debrief

19. Debrief: Similar Right Triangles
What is an altitude, and what happens when an altitude is drawn from the right angle of a right triangle?
What is the relationship between the original right triangle and the two similar sub-triangles?
Explain how to use the ratios of the similar right triangles to determine the unknown lengths of a triangle.