CP GEOMETRY MIDTERM STUDY GUIDE

CP GEOMETRY: MIDTERM STUDY GUIDE

Part 1: Chapter 1

• Statement Evaluation

  1. Points H, D, and E are collinear.

  2. Point G lies on 𝐻𝐷⃡.

  3. Points F, G, and B are coplanar.

  4. 𝐷𝐻 and 𝐷𝐺 are opposite rays.

• Value Calculations5. Find the value of x.6. Find the length of 𝐴𝐵̅̅̅̅.7. Find the length of 𝐵𝐶̅̅̅̅.

Part 2: Chapter 2

• Midpoint and Statement Evaluation8. Find the value of x.9. Find the length of 𝐴𝐵̅̅̅̅.10. Find the length of 𝐴𝐶̅̅̅̅.

• True/False Statements11. Plane AEH and plane BCG are parallel.12. 𝐷𝐶̅̅̅̅ and 𝐴𝐵̅̅̅̅ intersect.13. 𝐷𝐻̅̅̅̅ and ̅𝐸𝐹̅̅̅ are parallel.14. Plane BCD and plane AEH are parallel.15. 𝐸𝐻̅̅̅̅ and 𝐷𝐶̅̅̅̅ are skew lines.16. ̅𝐻𝐺̅̅̅ and ̅𝐸𝐹̅̅̅ are skew lines.

Part 3: Chapter 3

• Angle Measurements17. Find ∠EBF18. Find ∠DBF19. Find ∠DBE20. Find ∠ABF21. Find ∠EBA22. Find ∠DBC.

• Distance and Midpoint Calculations23. Find the distance between points (3, 4) and (-3, -4).24. Find the midpoint between points (-3, 3) and (5, 3).25. For segment ̅𝐷𝐸̅̅̅, one endpoint is D(6, 5) and the midpoint is M(4, 2). Find the coordinate of the other endpoint E.

Part 4: Chapter 4

• Properties and Statements26. Symmetric Property of Congruence: If 𝐴𝐵̅̅̅̅ ≅ 𝐶𝐷̅̅̅̅ , then ___________________.27. Distributive Property: −3(𝑥 − 7) = ____________________.28. Transitive Property of Congruence: If ∠X ≅ ∠Y, and ∠Y ≅ ∠Z, then ______________________.29. Multiplication Property of Equality: If 𝑥/7 = −4, then _____________________.30. Use the figure below to identify a pair of vertical angles, a pair of complementary angles, and a pair of supplementary angles.

Part 5: Chapter 5

• Angle and Triangle Classifications31. Find the value of x.32. Find 𝑚∠𝐴𝐵𝐷.33. Find 𝑚∠𝐶𝐵𝐷.

Additional Geometry Questions

• Angle Relationships34. If 𝑚∠1 = 119°, find the measures of the remaining angles.35. Find the value of x using the image below.36. Find the value of x using the image below.37. Write the equation in slope-intercept form: 5𝑥 − 6𝑦 = −12.

• Equations of Lines38. Find the slope between points 𝑆(−4, 5) and 𝑇(3, −9).39. Write the equation of the line in slope-intercept form parallel to 𝑦 = −1/3𝑥 + 1 through point (−1, 3).40. Write the equation of the line in slope-intercept form perpendicular to 𝑦 = 2𝑥 − 4 through point (−2, 2).41. Find x-intercept and y-intercept of 2𝑥 + 3𝑦 = −24.

Polygons and Triangle Properties

• Polygon Properties42. Write the line equation in point-slope form through points (1, 2) and (3, −2).43. Find the interior angle sum of a nonagon.44. Find the measure of one exterior angle in a regular hexagon.45. Difference between a concave polygon and a convex polygon.

Final Classifications and Calculations

• Triangle Classifications46. Find the measure of x for the irregular polygon.47. Classify the triangle with angles 65°, 21°, and 94°.48. Classify the triangle with sides 14 cm, 11 cm, and 14 cm.

• Congruency Statements and Proofs49. Using ⊿𝐺𝐻𝐼 ≅ ⊿𝐿𝑀𝑁, list pairs of congruent angles and sides.50. Write 2 triangle congruency statements for the image below.51. Using ⊿𝐿𝑀𝑃 ≅ ⊿𝑂𝑀𝑁, mark congruent angles and sides in the image.

Examples and Properties

• Postulates and Proofs52. State the postulate proving two triangles congruent for the three images.53. Complete the two-column proof below.54. Identify how the triangles are congruent (SSS, SAS, AAS, ASA, or HL) and complete a triangle congruency statement.

• Angle Measures55. Find 𝑚∠1, 𝑚∠2, and 𝑚∠3.56. Find the measure of x.57. Two characteristics of an equilateral triangle.

Triangle Midsegment Theorem

• Midsegment Problems58. Find values of x, y, and z using Triangle Midsegment Theorem with lengths 24, 36, and 38.59. If 𝐴𝐵̅̅̅̅ = 8, 𝐵𝑍̅̅̅̅ = 6, 𝑋𝑌̅̅̅̅ = 20, find segment lengths.60. If 𝐸𝐺 bisects ∠𝐷𝐸𝐹, find x and lengths of 𝐹𝐺̅̅̅̅ and ̅𝐺𝐷̅̅̅.

Additional Problems and Inquiries

• Angle Bisectors and Inequality61. If 𝑌𝑊 bisects ∠𝑋𝑌𝑍, find t and measure of 𝑚∠𝑊𝑌𝑋.62. Use Triangle Inequality Theorem to check if a triangle can have sides:

  • 14 in, 8 in, 6 in.

  • 3 cm, 4 cm, 5 cm.

  • 22 ft, 15 ft, 6 ft.

  63. Order the angles from smallest to largest.

• Sides Ordering64. Order the sides from longest to shortest.65. Find range of possible lengths for a third triangle side given two side lengths:

  • 11 cm, 4 cm.

  • 19 ft, 32 ft.

  • 5.6 m, 18.9 m.

Conclusion

• Final Thoughts: Remember to study hard, get a good night’s sleep, and have a nutritious breakfast. Trust yourself; you are more capable than you think!