Quarter 1 Study Guide Honors Geometry

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1 Name: Date: Period: Topic 1: Vocabulary Quarter 1 Study Guide Honors Geometry Date of Quarterly Assessment: Define geometric terms in my own words. 1. For each of the following terms, choose one of the following: a) Define the term in your own words b) Draw or write an example of the term Perpendicular Bisector Angle Bisector Congruent Complementary Supplementary Linear Pair Incenter Circumcenter Vertical Angles Topic 2: Angle Relationships Recognize when angles are complementary, supplementary, vertical, or a linear pair. Solve to find a missing value using the above relationships. 2. Find the measure of each angle. 3. Solve for x. 32

2 4. Solve for y. 5. Find the value of each angle. Topic 3: Parallel Lines and Transversals Recognize angle relationships formed by transversals, including: o alternate interior o alternate exterior o consecutive interior o consecutive exterior o corresponding o vertical o linear pair o congruent o supplementary Solve to find missing values using the above angle relationships. 6. Alternate angles are congruent / supplementary. (circle one) Consecutive angles are Corresponding angles are congruent / supplementary. (circle one) congruent / supplementary. (circle one) 7. Use the figure below to answer the following questions Name the alternate interior angle to 3. Name the consecutive interior angle to 13. Name a corresponding angle to 6. What is the relationship between 11 and 16? What is the relationship between 11 and 12? Name all angles that are supplementary to

3 8. Find the value of y. 9. Find the value of x. 10. Given l m, find the value of x. 11. Find the value of y. (9x 50) (x 2 9x + 31) Topic 4: Slopes Write the equation of a line from a graph. Write or graph a linear equation using slope and/or y-intercept. Determine when two slopes are parallel, perpendicular, or neither. 12. For each graph below, complete the following: a) Write the equation of the line shown. b) Write an equation of a line that is parallel to the given line. c) Write an equation of a line that is perpendicular to the given line.

4 13. Write the equation of the line that is parallel to the graph shown on the right and passes through the point ( 4,1). 14. Write the equation of the line that is perpendicular to the graph shown on the right and passes through the point (6,7). Topic 5: Proofs Use geometric properties and definitions to complete a 2-column proof. 15. Complete the proof.

5 16. Complete the proof x + 13 = 165 Substitution Property Subtraction Property Division Property Topic 6: Transformations Recognize and perform translations, rotations, and reflections. Recognize and write rules to represent transformations. 17. Use the figure on the right to complete the following transformations. a. Label each point on the pre-image. b. Reflect the shape across the x-axis. c. Translate the shape right 4 units. d. Label each point on the image.

6 18. Use the figure on the right to complete the following transformations. a. Label each point on the pre-image. b. Rotate the shape 270 about (1, 1). c. Label each point on the image. 19. Use the figure on the right to complete the following transformations. a. Label each point on the pre-image. b. Rotate the shape 90 about the origin. c. Label each point on the image. 20. Write a rule for the translation shown below. (x, y)

7 Topic 7: Polygons Determine the sum of the interior angles of a polygon. Solve for a value using interior angle properties. 21. What is the sum of the interior angles of a pentagon? 22. What is the sum of the interior angles of an 11-sided polygon? 23. Given the figure below, find the measure of D. 24. What is the measure of ONE angle of a regular hexagon? Topic 8: Bisector and Triangle Centers Apply the perpendicular bisector theorem. Construct the incenter and circumcenter of a triangle. 25. Use the figure below to answer the following questions. a. Find the length of segment EG. b. Find the length of segment EH. 26. Complete the following sentences. The circumcenter of a triangle is created by the and is equidistant from the of the triangle. The incenter of a triangle is created by the and is equidistant from the of the triangle.

8 27. Construct the circumcenter of each triangle below. If you use patty paper, attach it to the page.

a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles

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