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Name: ___________________________________ Date: 3/11/2014 Mr. Murpheyβs Analytical Geometry Block: 2 Standard: SWABAT Verify experimentally the properties of dilations given by a center and a scale factor (MCC912. G.SRT.1) Triangle Similarity Inbox Task - Solve each proportion. 1. π ππ 4. = π 2. π ππ ππ = π¨π© π π = 5. ππ π 3. ππ π.π πΈπΉ = π.π π.π π ππ 6. = π π+ππ πβπ ππ = π+π ππ 7. If βQRS ~ βXYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. Triangle Similarity: AA, SSS, SAS Fill in the blanks to complete each postulate or theorem. 1. If the three sides of one triangle are ____________________ to the three sides of another triangle, then the triangles are similar. 2. If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are ____________________. 3. If two angles of one triangle are ____________________ to two angles of another triangle, then the triangles are similar. Name two pairs of congruent angles in Exercises 4 and 5 to show that the triangles are similar by the Angle-Angle (AA) Similarity Postulate. 4. 5. ________________________________________ ________________________________________ Substitute side lengths into the ratios in Exercise 6. If the ratios are equal, the triangles are similar by the Side-Side-Side (SSS) Similarity Theorem. 6. GH JK ο½ HI GI ο½ ο½ ο½ ο½ οοοοοοοοοο οοοοοοοοοο KL οοοοοοοοοο οοοοοοοοοο JL οοοοοοοοοο οοοοοοοοοο Name one pair of congruent angles and substitute side lengths into the ratios in Exercise 7. If the ratios are equal and the congruent angles are in between the proportional sides, the triangles are similar by the Side-Angle-Side (SAS) Similarity Theorem. 7. ο½ PQ QR ο½ οοοοοοοοοο ο½ οοοοοοοοοο ο½ οοοοοοοοοο ο½ οοοοοοοοοοο ST TU In the diagram of the tandem bike, AE οΌοΌ BD . 8.Explain why ο²CBD οΎ ο²CAE. congruent angles: οοοοοοοοοο ____________________________________________ ____________________________________________ ____________________________________________ 9.Find CE to the nearest tenth. _____________________________________ Applying Properties of Similar Triangles Fill in the blanks to complete each theorem. 1. If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides ____________________. 2. If three or more parallel lines intersect two transversals, then they divide the ____________________ proportionally. 3. An ____________________ of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides. 4. If a line divides two sides of a triangle proportionally, then it is parallel to the ____________________. In Exercises 5 and 6, set up a ratio and substitute values from the figure to find each length. 5. LS ____________________ 6. BK _____________________ Complete Exercises 7 and 8 to verify that HI οΌοΌ XY . 7. Check that the sides are proportional. JX JY ο½ ο½ ο½ ο½ _______ _______ _______ _______ XH YI 8. If the two ratios in Exercise 7 are equal, then sides HJ and IJ are divided proportionally. If the sides are proportional, then HI is parallel to XY . Tell whether HI is parallel to XY . ________________________________ Use the figure for Exercise 9. The figure shows part of a freeway interchange. The raised freeway is supported by vertical, parallel pillars. Set up a ratio and solve to find the length. 9. Use a calculator to find AQ to the nearest tenth of a yard. ________________________________________ In Exercises 10 and 11, set up a ratio and substitute values from the figure to find each length. 10. CE ____________________ 11. XZ _____________________ 1.Is GF οΌοΌ HJ if x ο½ 5? Explain. 3. Find the length of BC . 4. The figure shows three lots in a housing development. If the boundary lines separating the lots are parallel, GF to the nearest tenth?