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Geometry Semester 1 Review Name: 1. For each of the geometric statements below, write in words what the statement is representing and then draw a picture of the geometric statement. Geometric Statement What is this saying? Draw a picture PQ AB l || m jk PRS Z 2. Given the dilation to the right, answer the following questions: a) Name all of the pairs of sides which are parallel to each other: B' ______ || _______, _______ || _______, _______ || ______, ______ || ______ b) Given that the scale factor is 3 and AB is 12 centimeters, what is A’B’? D' B D C A A' 3. Name all of the valid postulates or theorems that can be used to prove that two triangles are congruent. C' 4. For the following triangles, determine whether they are congruent and by which theorem or postulate. If they are not congruent, explain why not. 5. Write a congruent statement for the following triangles: 6. Using the triangle from above left, complete the following congruence statements: QRS _____; CDS _____; DS _____ ; RS _____ DC _____ 7. What additional information would be needed to prove the triangles are congruent using ASA? 8. Draw a picture to solve for x in the following problem: mD 2 x 33 ; mS 2 x 6 . EFH DPS , mE 5x 6 ; Use the following picture for questions 9-11. The original triangle is in grey. 9. For each of the triangles, describe the transformation and then write a general rule for the transformation shown. Triangle Number Describe Transformations Write a Rule 1 (x, y) ( , ) 2 (x, y) ( , ) 3 (x, y) ( , ) 4 (x, y) ( , ) 5 (x, y) ( , ) 6 (x, y) ( , ) 10. Which of the triangles are congruent to the original? _____________________________ 11. Which of the triangles are similar to the original? _______________________________ Use the following diagram for questions 12-18. a 1 2 3 4 b 6 5 8 a || b . 12. Name all the pairs of vertical angles. 13. Name all the pairs of same-side interior angles. 7 14. Name all the alternate interior angles. 15. Name all the corresponding angles. 16. Name 4 linear pairs. 17. Which of the above types of angles are congruent? supplementary? 18. Which of the above type are 19. Complete the following proof using the figure from above: Given: a || b Prove: m1 m8 180 Statements 1. 2. m5 m8 180 Justifications 1. 2. 3. 3. Corresponding angles of parallel lines are congruent 4. 4. 20. Solve for x in the diagram below. 21. Select all the statements that are true for similar figures: A) All the corresponding angles have the same ratio. B) All the corresponding sides have the same ratio. C) All the corresponding angles are congruent. D) All the corresponding sides are congruent.