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Geometry REVIEW: Chapter 1 Name ___________________________________ 1. How many planes can be drawn through any three noncollinear points? 1 plane For numbers 2 and 3, use the figure at the right. 2. Which three points in the figure are collinear? F, E, G 3. Name the intersection of the plane P and the plane that contains points B, C, and D. BC ����. Write your answer as a reduced mixed number. 4. Find the length of 𝑅𝑆 5 1 in 16 5. Given A is between Y and Z and YA = 5.5, AZ = 2x, and YZ = 41.5, find AZ. AZ = 36 ���� . 6. Find the length of 𝑃𝑄 7. Find the distance between P(2, 8) and Q(5, 3). Write your answer in simplified radical form. 34 PQ = 25.7 cm 8. Find the value of y if B is between A and C, AB is 2y, BC is 6y, and AC is 48. y=6 ���� if L(8, 5) and B(–6, 2). 9. Find the coordinates of the midpoint of 𝐿𝐵 7 (1, ) 2 10. Graph the ordered pairs A(-2, 3), B(3, 3) and C(2, -1). Then find the area and perimeter of the figure formed. Round all values to the nearest tenth. 14.8 u Perimeter: 10 u2 Area: For numbers 11 and 12, use the figure at the right. 11. Classify ∠ABC as acute, right, obtuse, or straight. obtuse 12. ED bisects ∠GEF. If m∠GED = (2x – 8)° and m∠DEF = 80°, find the value of x and m∠GEF. x = 44, m<GEF = 160◦ 13. Which figure best represents the first step in constructing the bisector of PQ ? a) b) A c) d) For numbers 14-18, use the figure at the right. 14. Find m∠FBD if ∠FBD and ∠DBE are complementary and m∠FBD is twice m∠DBE. m<FBD = 60◦ 15. Which pair of angles are supplementary? answers vary 16. Which angle is a vertical angle to ∠ABE? <CBD ���� ⊥ 𝐵𝐹 ���� . 17. If m∠CBF = (6x + 18)°, find the value of x so that 𝐶𝐵 x = 12 18. Find m∠ABC if m∠ABC = (4x + 9)° and m∠EBD = (7x – 9)°. m<ABC = 33◦ 19. Classify the figure below by the number of sides it has, then determine if it is concave or convex, then determine if it is regular. hexagon; concave; irregular 20. Find m∠A if ∠A is complementary to ∠B, ∠B is supplementary to ∠C, m∠B = (15x – 2)°, and m∠C = (25x + 22)°. m<A = 32◦ 21. A student uses a straightedge and a compass to perform a construction given ∠QPS. Which type of construction is best represented in the figure? angle bisector