Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Noether's theorem wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euclidean geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Geometry 6.5 SWLT: Use the SSS & SAS Similarity Theorems Side-Side-Side (SSS) Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar. If AB BC CA , then ABC RST = = RS ST TR A R B C S T Using the SSS Theorem Which is Similar to ABC? D 6 4 A 8 B E 24 J 9 12 F 8 C H 16 18 G Compare the Triangles by finding the ratios of the corresponding Sides ABC DEF? Shortest Sides ABC GHJ? Shortest Sides AB 8 = =2 DE 4 AB 8 1 = = GH 16 2 Longest Sides Longest Sides BC 12 3 = = EF 8 2 Remaining Sides AC 9 3 = = DF 6 2 The ratios are not the same, so ABC is not similar to DEF BC 12 1 = = HJ 24 2 Remaining Sides AC 9 1 = = GJ 18 2 All ratios are equal, ABC GHJ Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that form these angles are proportional, then the triangles are similar If ÐX @ ÐM and ZX XY = PM MN , then XYZ MNP M X N Y Z P Using SAS… is PRQ TSR? PRQ and SRT are vertical angles, are congruent P Find the Ratios of the corresponding sides 18 Longer Sides PR 18 3 = = TR 24 4 The corresponding sides proportional, so PRQ TRS 12 R Shorter Sides QR 9 3 = = SR 12 4 S 9 Q 24 T