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Name_________________________________ Date___________ Word List and Review Packet for Geometry Midterm Vocabulary word 180° Definition Picture 90° AAS Congruence Acute angle Acute triangle Adjacent angles Alternate exterior angles Alternate interior angles 1 Vocabulary word Angle Definition Picture Angle bisector – show the construction Base Base angle Centroid Circumcenter Collinear Complementary angles Conclusion 2 Vocabulary word Conditional statement Definition Picture Congruent Conjecture Consecutive interior angles Converse statement Coplanar Corresponding angles Counterexample Deductive reasoning 3 Vocabulary word Dilation Definition Picture Enlargement Equiangular triangle Equilateral triangle Exterior Angle Hypothesis H-L Congruence Theorem Incenter Interior angle 4 Vocabulary word Intersection Definition Picture Inverse Statement Isometry Isosceles triangle Line Linear pair Midpoint Midsegment – show how to create the perpendicular bisector of a segment Obtuse angle 5 Vocabulary word Obtuse triangle Definition Picture Parallel lines Perpendicular lines Plane Point Proof Proportions Ratio Ray 6 Vocabulary word Reason Definition Picture Reduction Reflection Reflexive property Right angle Right triangle Rotation SAS Scale Factor 7 Vocabulary word Scalene triangle Definition Picture Segment Side Similarity SSS Congruence Statement Supplementary Angles Transformation Transitive Property 8 Vocabulary word Translation Definition Picture Transversal Triangle Vertex Vertex Angle Vertical angles 9 Name______________________________ Date__________ Triangle review: Short Answer Identify all triangles in the figure that fit the given description. 1. equilateral 2. isosceles Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theorem you would use. 3. 3. 4. 5. Find the value of x. 6. 7. 8. 9. 10. 11. 10 12. 12. 13. The vertices of a polygon are given. Find the coordinates of the vertices of the image after the specified translation. 14. A(–2, –1), B(–3, 4), C(–1, 3), D(–1, –1); (x, y) (x – 4, y – 2) Solve. 15. 16. 17. Complete. 18. If 19. , then If _____?_____. , then . Use the diagram to find x. 20. 11 Questions 21-25, use the diagram on the right: Given: . 21. Find the scale factor of ABCD to WXYZ. 22. Find the scale factor of WXYZ to ABCD. 23. Find the values of s, t, and u. 24. Find the perimeter of each polygon. 25. Find the ratio of the perimeter of ABCD to the perimeter of WXYZ. Are the triangles similar? If so, state the similarity and a postulate or theorem that can be used to prove that the triangles are similar. 26. 27. 29. 28. 30. For questions 21-25 use the diagram at the right: 31. 34. 32. 35. 33. 12 The vertices of a polygon are given. Find the coordinates of the vertices of the image after a dilation having the given scale factor. 36. A(–6, 2), B(2, 2), C(2, 0), D(–6, 0); k = 0.5 37. P(–8, 4), Q(4, 4), R(0, –4), S(–4, –4); k = For questions 38-42 use the diagram at the right, Given: 38. Find the scale factor of ABCDE to VWXYZ. 39. Find the scale factor of VWXYZ to ABCDE. 40. Find the values of r, s, t, and u. 41. Find the perimeter of each polygon. 42. Find the ratio of the perimeter of ABCDE to the perimeter of VWXYZ. 43. of has vertices A(0, –3), B(3, 1), and C(3, –3). Find the coordinates of the vertices of the image after a dilation having a scale factor of 3. Then find the perimeter of the image. 44. The ratios of the side lengths of triangle ABC are 7:9:12 (AB:AC:BC). Solve for x. 13 Complete the proof. 1. Given: Prove: 2. Given: Prove: 14 3. Given: Prove: 4. Given: , Prove: 5. If , show that . 15 Perform the following transformation on the triangle in order. a) Translate the triangle (x, y) → ( x + 9 , y – 10) b) Reflect the triangle over the x-axis c) Rotate the triangle 180° clockwise 16 17