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

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!**

Lesson 15: Review

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.

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?

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.)

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

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:

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!**

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:

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

Right Triangle Ratios

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?

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

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?

Creating Right Triangle Ratios

Exit Ticket

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

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.