Bellwork Determine whether the triangles are similar. A B
Bellwork The triangles are similar. Find the values of x and y. A B C A. x = 5.5, y = 12.9 B. x = 8.5, y = 9.5 C. x = 5, y = 7.5 D. x = 9.5, y = 8.5 A B C D
Unit 5 Lesson 2 Triangle Similarity Honors Geometry Unit 5 Lesson 2 Triangle Similarity
Similar Triangles Showing that triangles are similar is very much like showing that they are congruent We will use “shortcuts” A special combination of congruent angles and proportional sides There are 3 shortcuts
First, Keep in mind, if two angles from the triangles are congruent, what must be true about the third? Notice the similarity statement!
Next Notice the sides are proportional, not congruent!
Finally, The congruent angles must be between the proportional sides!
Similar Triangles? Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. ΔQXP ~ ΔNXM by AA Similarity.
Similar Triangles? Determine whether the triangles are similar. If so, write a similarity statement. A. Yes; ΔABC ~ ΔFGH B. Yes; ΔABC ~ ΔGFH C. Yes; ΔABC ~ ΔHFG D. No; the triangles are not similar. A B C D
Similar Triangles? Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. By the Reflexive Property, M M. ΔMNP ~ ΔMRS by the SAS Similarity Theorem.
Determine whether the triangles are similar Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A. ΔAFE ~ ΔABC by SSS Similarity Theorem B. ΔAFE ~ ΔACB by SSS Similarity Theorem C. ΔAFE ~ ΔAFC by SSS Similarity Theorem D Not Similar A B C D
Determine whether the triangles are similar Determine whether the triangles are similar. If so, choose the correct similarity statement to match the given data. A. ΔPQR ~ ΔSTR by SSS Similarity Theorem B. ΔPQR ~ ΔSTR by SAS Similarity Theorem C. ΔPQR ~ ΔSTR by AAA Similarity Theorem D. The triangles are not similar. A B C D
Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar? A. = B. mA = 2mD C. = D. = ___ AC DC __ 4 3 BC 5 EC A B C D
Use Similar Triangles to Solve using proportion ALGEBRA Given , RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT. Answer: RQ = 8; QT = 20
ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.
Within One Triangle… Similarity can exist inside of a triangle Proportional Parts… Special Segments Midsegments
A Segment Parallel to one side This segment can be drawn parallel to any one of the three sides
Find the Length of a Side
Midsegment The midsegment is half the length of the side that its parallel to
Use the Triangle Midsegment Theorem In the figure, DE and EF are midsegments of ΔABC. Find AB. ED = 1/2 AB 5 = 1/2 AB 10 = AB
A B C D In the figure, DE and DF are midsegments of ΔABC. Find BC.
A B C D In the figure, DE and DF are midsegments of ΔABC. Find DE.
No triangle at all… The same ratio is cut into every transversal
Use Proportional Segments of Transversals MAPS In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.
In the figure, Davis, Broad, and Main Streets are all parallel In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in between city blocks. Find x. A. 4 B. 5 C. 6 D. 7 A B C D