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Unit 1B: Congruence and Similarity MATH 8 STUDY GUIDE Name ___________________________________ Period _______ Date ____________ Knowledge: Draw a picture to assist you if needed. Write answers on a separate piece of notebook paper. 1. 2. 3. 4. 5. Which transformations are congruent to the original figure? Translation, Rotations and Reflections Which are similar to the original figure? Dilations How many angles are formed when a transversal intersects 2 parallel lines? 8 anglers How many different angle measures will there be? Two different measures – one will be acute and one will be obtuse Name and draw a picture to show each special angle pair created when 2 parallel lines are cut by a transversal (there are 5 special angle pairs). Alternate Interior, Alternate Exterior, Corresponding Angles, Same-side Interior, Same-side Exterior What is the sum of the interior angles of any triangle?180 degrees What is the sum of the exterior angles of any triangle? 360 degrees What is the relationship between an exterior angle of a triangle and the 2 opposite interior angles? The exterior angles is the sum of the two non-adjacent (remote) interior angles. Dilation: 6. Draw a dilation of the figure using the scale factor of ¼. Name the new coordinates. 7. Draw a dilation of the figure using the scale factor of 2. Name the new coordinates. A’ (0,1) B’ (1,-1) C’ (-1, -1) A’ (4,0), B’ (0,-4), C’ (-4, 2), D’ ( 2, 4) Parallel Lines Cut by a Transversal: 8. Given: m || n. What is the m 2 ? _85_________ 9. Given: PQ RS . What is m∡1. _115_______ (b) Name the relationship between the angles? __Corresponding Angles_____________________________ 65 P 85 m R S 1 2 n 10. Using the figure to the right, name a pair of angles that are: a) Alternate interior _3,6 and 4,5_______________ b) Alternate exterior _1,8 and 2, 7________________ c) Same-side exterior _1,7 and 2,8_________________ d) Vertical 1,4 2,3 5,8 6, 7________________________ e) Same-side interior _3,5 and 4,6______________ f) Supplementary 1,2 2,4 3,4 1,3 6,8 8,7, 7,5 5,6_______________ 93° 1 3 5 7 6 8 Q 2 4 g) Corresponding _1,5 3,7 2,6 4,8______________ Triangle Angles 11. Find the missing measure. 12. Find the measure of angle a. Explain how you found it. 39 102 33 a 45 63° 78° 13. Solve for the given variable. 14. 160 If Marietta had the following 5 roads with the given miles, how many miles would “x” be? 3 miles 2 miles 6 miles 15. Find the measure if the missing angle. X=9 x miles 16. Determine if the triangles are similar. Solve for a. The missing angle measures 40 3 a 5 15 a9 140˚ x + 60 17. Based on these triangles being similar, find find the scale factor of the smaller triangle to the Larger triangle. 6 18. Based on the similar triangles below, find the missing angle. 14 7 The scale factor is 2 3 x 2 20 2 x 60 x 30