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Adv. Geometry: A review for you to do Answer with problems 1 – 8 with Always, Sometimes, Never. For the answer “Sometimes” give an example of when the statement is true and when it is false. 1. A line intersects with a plane at exactly one point. 2. 2 distinct planes intersect at a line. 3. Three planes intersect at a point. 4. Three planes intersect at a line. 5. Three points are contained in exactly one plane 6. Two distinct lines are contained in one plane. 7. Two intersecting lines and a point are contained in exactly one plane. 8. Three lines are coplanar M is the midpoint of LR . 9. LM = 2x + 3, MR = 3x-1 LR = ______________ 10. L has a coordinate of 15. LR = 6. What is/are the coordinates of M? _________ HT bisects LHR creating angles 1 and 2. 11. LHR is 48 degrees. How many degrees is angle 2? 12. m LHR = 5x + 18, m 1 = 3x + 4. Find the measure of angle 2. A 1 C 5 F 2 E 3 4 D B 17. DEB is a right angle. m1 8x 10 , m3 4x 8 . Find m2 . m2 = _______ 18. Let EF bisect AED. m4 19x 1 and m3 9x 3 . Find m2 . m2 = ____ Chapter 2 to help give you a clue True or False: (If false, provide a counter example) 1. If 2 angles are congruent, then they are vertical angles. (T or F) Converse ___________________________________________ (T or F) 2. Two angles are supplements if and only if the sum of the 2 angles is 180 degrees. (T or F) 3. B C A 5 2 3 1 F 4 D E b. Given: AE BF Prove: 5 is complementary to 3 Statements Reasons 4. A supplement of a given angle is 10 less than three times as large as a complement of the angle. Find the measure of the given angle. 5. B is the midpoint of EC . Point D is in the interior of angle ABC such that BD bisects ABC . mDBC = 15 degrees. Find mEBA . (Draw, label and solve) A B 6. Given: AC BD Prove: AB CD C D Statements Reasons 7. Use the same picture for a, b and c. Y R X 2 1 3 S 8 Z 4 W 7 5 6 T V U a. Given: 1 and 2 are complementary; 6 and 8 are complementary Prove: ZX bisects YZW Statements Reasons If 7 XZW, which one of the following statements must be true? b. a. SZX SZV c. 1 6 b. TX RV d. 2 5 c. Which of the following would allow you to deduce that TX RV in the same picture above? ZS bisects RZT and ZW bisects XZV 1 and 5 are complementary 3 and 7 are complementary RZX and TZV are supplementary