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Name: ___________________________________________ Chapter 1 Review Sheet Date: ____________________________ Geometry Advanced Chapter 1 Key Topics Section 1.1 Section 1.2 Visual and number patterns Steps of Inductive Reasoning Making conjectures and finding counterexamples Section 1.3 Section 1.4 Segment Addition Postulate Distance Formula Section 1.5 Point, line, plane, ray, initial point, opposite rays, segments and endpoints collinear, coplanar intersections sketches Angles: acute, obtuse, right, straight Angle Addition Postulate Section 1.6 Midpoint Formula Segment and angle bisectors Congruence Vertical angles, linear pairs Complementary angles, supplementary angles Section 2.1 – 2.2 Conditional, inverse, converse, contrapositive, and biconditional statements ALGEBRA SKILLS YOU NEED TO KNOW: 1. Factoring 2. Systems of Equations 3. Simplifying Radicals Chapter 1 Practice 1. Describe the pattern and predict the next 2 terms. a. -2, -7, -17, -32, … b. 0, 2, 6, 14, 30, … 2. Draw the next figure in the pattern. , , ,… 3. Complete the sentence. a. If three points lie on the same line, then they are _________________. b. If two angles have a sum of 90 degrees, then they are ________________. 4. Write the converse, inverse, and contrapositive of the statement for 3a. 5. a. Make a conjecture based on the results. b. Show the conjecture is false. Given points A, B, C, and D with AB, BC , CD, and DA drawn the result is always a 4-sided shape. 6. Draw 5 coplanar points, A, B, C, D, and E so that BA and BC are opposite rays, and DE intersects AC at B. 7. Given two points A (5, -3) and B (-3, 1), find a) the midpoint of AB b) the length of AB 8. Given the midpoint M (-8, 11) of FE and endpoint E (2, -7), find the coordinates of the other endpoint F. (Show the algebraic steps. In other words, do not just count) 9. Use the figure to the right to answer questions a – c. a. Name 4 points that are not coplanar. b. Name 3 points that are coplanar but not collinear. c. Name 2 lines are intersect but are not coplanar. 10. For questions a – c, use the diagram shown. a. If m KJM = 145o, m KJL = 6xo, and m LJM = (3x + 10)o, find x. b. If m KJM = (3x2 – 2x)o, m KJL = (x2 + 11)o, and m LJM = (3x + 1)o, find x. (Make sure your answer is reasonable!) 11. BT bisects ABC. Find x. 12. S is between T and V. R is between S and T. T is between R and Q. QV = 23, QT = 8, and TR = RS = SV. Find RS, QS, and TS. RS = ______ QS = ______ TS = ______ 13. Use the figure to the right to answer a – c. a. List all pairs of vertical angles. b. List all angles that are linear pairs. c. If m 9 = 36o what are the measures of the other 3 angles? 14. Find the value of the variables. 15. A and B are complementary. Find m A and m B if m A = (x2 – 19)o and m B = (8x + 4)o 16. The measure of an angle is 5 less than 4 times the measure of its supplement. Find the measure of both angles. 17. Write the following statement into if-then format. Write a converse of the statement. Determine if the converse is true or false. If converse is true, write a biconditional of the statement. If converse is false, show it is false by counterexample. Two line segments with the same length are also congruent.