* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 8.2 Similarity
Survey
Document related concepts
Multilateration wikipedia , lookup
Noether's theorem wikipedia , lookup
Golden ratio wikipedia , lookup
History of geometry wikipedia , lookup
Technical drawing wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Penrose tiling wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Euler angles wikipedia , lookup
Rational trigonometry wikipedia , lookup
Four color theorem wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Trigonometric functions wikipedia , lookup
Apollonian network wikipedia , lookup
Euclidean geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Transcript
8.3 Methods of Proving Triangles Similar Objective: After studying this section, you will be able to use several methods to prove triangles are similar. Postulate If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the three angles of another triangle, then the triangles are similar. (AAA) Theorem If there exists a correspondence between the vertices of two triangles such that the two angles of one triangle are congruent to the two corresponding angles of other, then the triangles are similar. (AA) Given: A D B E A Prove: ABC ~ DEF D E B F C Theorem If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of corresponding sides are equal, then the triangles are similar. (SSS similarity) A Given: AB BC AC DE EF DF Prove: ABC ~ DEF D E B F C Theorem If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar. (SAS Similarity) AB BC Given: DE EF B E Prove: ABC ~ DEF A D E B F C Given: parallelogram YSTW D C Prove: BFE ~ CFD F A B E Given: LP EA L N is the midpoint of LP N P and R trisect EA Prove: PEN ~ PAL E P R A Given: KH is the altitude to J hypotenuse GJ of right GHJ Prove: KHJ ~ HGJ G K H The sides of one triangle are 8, 14, and 12, and the sides of another triangle are 18, 21, and 12. Prove that the triangles are similar. Summary: If you were to draw a triangle and have a line parallel to the base,creating two triangles, would the triangles be similar if you had a right triangle? Obtuse? Acute? Why? Homework: worksheet