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Similar Triangles Sydni Jordan - Olivia Smith Warren Mott High School 9B 1 rade evel ontent xpectation G. Geometry TR. Transformations and Symmetry 07. Grade 7 05 5th Expectation MMSTC 2 G.TR.07.05 Show that two triangles are similar using: AA similarity SAS similarity SSS similarity Use these criteria to solve problems and to justify arguments. MMSTC 3 Terms to Know Similar: Whenever two orhave more objects AA: Congruent: Corresponding: way to When prove having objects triangles the same are the similar exactusing SAS:AWay SSS: Way of proving proving triangles triangles are are similar similar have proportional sides and congruent when same relationship size/shape they have two pairs of two pairs when theyof have proportional 3 pairs of sides proportional and one pair angles angles of congruent angles sides 5 in. 55in. in. 5 in. 2 in. 5 in. 2in . 2 in. MMSTC 4 Proportionality When corresponding sides of a triangle have the same ratio 6 cm 3 cm 4 cm MMSTC 8 cm 5 AA Angle–Angle Similarity Corresponding angles must be congruent MMSTC 6 AA Similarity MMSTC 7 8 SAS Side-Angle-Side similarity Sides have to be proportional and corresponding angles have to be congruent MMSTC 9 SAS 2 in 3 in MMSTC 2 in. 3 in 10 3 in. 11 SSS Side-Side-Side Similarity Corresponding sides must be proportional MMSTC 12 SSS 8 in. 10 in. 4 in. 6 in. MMSTC 5 in. 3 in. 13 What Not To Use Wrong methods to use ASA SSA AAS 14 4,000 ft. 5,000 ft 400 ft. 3,000 ft. MMSTC 500 ft. 300 ft. 15 Review Proportionality 6 cm 3 cm AA 4 cm 8 cm MMSTC 16 Review SAS SSS 8 in. 10 in. 6 in. 4 in. 5 in. 3 in. 17 Resources • B, Christian. "Applying Similar Triangles to the Real World." similartraiangles3. PBWorks, 2010. Web. 28 Feb 2012. <http://similartriangles3.pbworks.com/w/page/23053498/ Applying Similar Triangles to the Real World>. • Michigan. Michigan Department of Education. Mathematics Alignment At A Glace. Michigan: Michigan, Web. <http://www.michigan.gov/documents/alignment_at_a_gl ance-7thweb_134801_7.doc>. MMSTC 18 MMSTC 19 Choose a Box! 1 2 3 4 5 6 21 Are these triangles similar? Yes 10 cm 4 cm 7 cm No 4 cm Return 10 cm 7 cm 22 For these triangles to be similar, what must the length of the missing segment be? 1.5 in. ? 5 in. 10 in. Return 4 in. 2 in. 8 in. 2.5 in. 3.5 in. 23 Which method can be used to find out if these two triangles are similar? AA 60º SSS 3 cm 2 cm 75º Return 45º 75º SAS 24 If you have two pairs of congruent angles in two triangles, which similarity can be used to prove that they are similar? SAS Return AA SSS 25 Are these triangles similar? 45º 45º 8 in. YES 4 in. NO 7 in. Return 3.5 in. 26 Which one is not a way to prove that triangles are similar? AA Return SSA SAS 27 CORRECT! 28 INCORRECT! 29