B. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division

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1 . efinitions 1) cute angle ) cute triangle 3) djacent angles 4) lternate exterior angles 5) lternate interior angles 6) ltitude of a triangle 7) ngle ) ngle bisector of a triangle 9) ngles bisector 10) ase of an isosceles triangle 11) ollinear 1) omplementary angles 13) ongruent angles 14) ongruent polygons 15) ongruent segments 16) ongruent triangles 17) onsecutive interior angles 1) ontrapositive 19) onverse 0) onvex polygon 1) oncave polygon ) orollary 3) orresponding angles 4) ounterexample 5) decagon 6) diagonal of a polygon 7) distance between points ) equiangular triangle 9) equiangular polygon 30) equilateral polygon 31) equilateral triangle 3) exterior angle 33) exterior of an angle 34) heptagon 35) hexagon 36) hypotenuse 37) hypothesis 3) interior angle of a polygon 39) interior of an angle 40) intersecting lines 41) isosceles trapezoid 4) isosceles triangle 43) kite 44) leg of an isosceles triangle 45) leg of a right triangle 46) linear pair 47) line perpendicular to a plane 4) measurement of an angle 49) median 50) midpoint 51) midsegments of a trapezoid 5) midsegments of a triangle 53) n-gon 54) negation 55) nonagon 56) obtuse angle 57) obtuse triangle 5) octagon 59) opposite rays 60) parallel lines 61) parallelogram 6) parallel planes Name 63) pentagon 64) perpendicular bisector 65) perpendicular lines 66) polygon 67) quadrilateral 6) ray 69) rectangle 70) regular polygon 71) remote interior angles 7) rhombus 73) right angle 74) right triangle 75) scalene triangle 76) segment 77) segment bisector 7) skew lines 79) square 0) straight angle 1) supplementary angles ) transversal 3) trapezoid 4) vertical angles 5) vertex of a triangle 6) vertex angle of an isosceles triangle. lgebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division. Formulas Slope formula Midpoint formula istance formula Point slope formula Slope intercept formula Slope of parallel lines Slope of perpendicular lines Sum of the interior angles of a convex polygon Sum of the exterior angles of a convex polygon Measure of one interior angle of a regular polygon Measure of one exterior angle of a regular polygon. Listings List the things that can and cannot be assumed from a figure List the undefined terms of geometry List all properties of parallelograms, rectangles, rhombi, and squares List all the properties of trapezoids, isosceles trapezoids, and kites List the ways to prove triangles congruent

2 Solve the following: 1) M is between L and N. Find ML and MN. 1 ML MN and LN 5. 4 ) M is between L and N. Find LM and LN. 1 LM LN and MN ) GFI is a right angle. mjfh m FJ, mfj (4x 1), mfh (10 x ), Find m FJ 4) GFI is a right angle. mjfh m FJ, mhfg (3x ), mhfi (5x 16), Find m HFG #3-#4 F G J I H 5) YM bisects XYZ, Find m MYZ. m XYZ x 6, m XYM (7x 4). Y #5-#6 Z 3x 6) YM bisects XYZ, mmyz 3( x ), mxyz. Find m XYZ. X M 7) MNO is an isosceles triangle with vertex M. MO x 7, NO 4x 6, mo 5x. The perimeter of MNO 76, find m O. ) The ratio of the measure of an angle to its supplement is 4:5. Find the measure of the angle and its supplement. 9) The measure of the complement of an angle is 10 more than 3 times the measure of the angle. Find the measure of the angle and its complement. 10) bisects, m 64.. Find x and y. #10 x 11).. Find x and y. In 1 and 13, determine the values of x and y for which a b. #11 47 x 0 y y 1) m3 ( x y ), m6 ( x y ), m ) m 63, m3 ( x 3 y ), m6 (7x y ). b a #1-# t

3 14) The measure of the angles of a triangle are represented by x 15, x, and 3x 5. Find the measure of each angle. 15) Given a right triangle with an altitude drawn to the hypotenuse. Find x. 16) ompare m 1 and m 3. ompare m 6 and m. ompare m 7 and m 1. 17) Find the sum of the measures of the interior angles of a polygon with 1 sides. x #15 54 # ) Find the sum of the measures of the exterior angles of a polygon with 19 sides. 19) Find the number of sides in a polygon whose interior angles have a sum of ) Find the measure of one interior angle of a regular polygon with 16 sides. 1) The measure of one interior angle of a regular polygon is 160. Find the number of sides. ) The measure of one exterior angle of a regular polygon is 4. Find the number of sides. 3) Find the measure of one exterior angle of a regular polygon with 13 sides. 4) NO is a midsegments of trapezoid LMPQ with bases LM and PQ. NO 3x 4, LM x 3, PQ 37. Find NO and LM. 5) F and H are midpoints of G and GI respectively in GI. FH x, I x 7. Find FH and I. 6) If sides of a triangle have lengths of 7 and 13, find the possible lengths of the third side. 7) Write a conditional sentence for square is a rectangle. ) State the hypothesis and the conclusion of problem 7. 9) Is the conditional true? Why or why not? 30) Write the converse of problem 7. 31) Is the converse true? Why or why not? 3) Write the contrapositive of problem 7. 33) Is the contrapositive true? Why or why not?

4 34) Name the parallelogram with only: a. diagonals perpendicular and congruent. b. diagonals congruent. c. diagonals that bisect opposite angles. 35) What is the exterior angle theorem? 36) How many lines can be drawn through exactly points? Justify your answer. 37) How many planes can be drawn through exactly 3 non collinear points? Justify your answer. 3) Write the negation of the statement Tomorrow is my birthday 39) What is the difference between inductive reasoning and deductive reasoning? 40) re XYZ and ZXY the same angle? Justify your answer. 41) oes mmno monp m MNP? Justify your answer. 4) Is the sum of three acute angles always an obtuse angle? Justify your answer. 43) oes the bisector of an obtuse angle always form acute angles? Justify your answer. 44) an a right triangle be isosceles? Justify your answer. 45) an an obtuse triangle be a scalene? Justify your answer. 46) an the supplement of a right angle be an acute angle? Justify your answer. 47) If one segment is a bisector of a second segment, will the second segment be the bisector of the first? Justify the answer. 4) re rectangles rhombi? Justify your answer. 49) re squares rectangles? Justify your answer. 50) re trapezoids quadrilaterals? Justify your answer. 51) re parallelograms trapezoids? Justify your answer. 5) o the diagonals of a trapezoid bisect each other? Justify your answer. 53) Given triangle with (,4); (-3,6), (1,3) a. Find the equation of the median. b. Find the equation of the altitude from point. c. Find the equation of the perpendicular bisector to side. 54) K is between L and N. If LK = 36 and KN = 10, then LN =? 55) Segment has endpoints at (,6) and (10,0). Its midpoint, M, is 56) Given: XM bisects X. If mxm = x + 7 and mmx = 4x 5, find mx.

5 Find the values for x. 7 57) 5) 50 x (3x + 9) 59) Factor the following equation. x 13x 60) Solve the following System. 3x 5y 3 ; 4x 5y 16 61) Factor the following equation. 5x 17x 6 6) Factor the following equation. 10x 7x 5 x x 1 63) Solve ) If m1 = 3x + 16 and m = 6x + 1, then x =? #64 1 #65 65) If mrmk = 5x +, mkmt = 3x 5, and mtml = 6x + 17, then x =? M Find the value of x. L T K R #66 6 #6 (x + ) x + 11 x (x + 5) (6x + 4) 4x x x # #71 x #67 (3x 10) 115 #69 5x 6 (x + 1) 7) List the sides of in order from shortest to longest. m = 10x;m = 5x 17;m = 7x 1

6 73) Use the figure below to find the indicated angle measures. a ll b c ll d m6 = 36 m1 = 13 m = a m3 = m4 = m5 = m13 = m15 = m16 = b m17 = m1 = c d Find the values for x and y. 74) 75) 3y l l 30 (x 14) (4x +) m m 6y t 76) Given: l m ;t s Prove: ) Given: l m ; 7 10 Prove: t s l m t s #76 #77 W X 7) Given: N X ; WV bisects NX Prove: WMN VMX M N V 79) Given: F ; ;F ; F Prove: F

7 F R 0) Given: is the midpoint of, F,,F. Prove: F 1) Given: R, R bisects. Prove: R R ) Given: bisects, bisects. Prove: T R Q S 3) Given:, and is the midpoint of. Prove: 4) Given: TQ bisects Prove: TQ bisects RS RTS,TQ RS. are right angles, 5) Given:,,. Prove: Solve the following Quadratics. 6) 1x 5x 7 0 7) 1x 1x 4 0 ) 9x 6x 0 9) 14x 50x 4 0 Solve the following systems. 90) y 3x 10 x 30 5y 91) x y x 5y 4 9) 5x y 1 4x 5y 1 93) 3x 56 4y y 1x ) Write an equation of a line is slope intercept form that goes through the points (5,3) and (7,-). 95) Write an equation of a line that is parallel to the line y=4x + 4 and goes through the point (3,-6). 96) Write an equation of a line that is perpendicular to y=-4x+6 and goes through the point (5,3). 97) Write an equation of a line that goes through the midpoint of segment (4,) and (,-) and is perpendicular to the segment. Write an algebraic proof for each of the following 9) 5x 3 4 x 99) 14 x x 100) 4 x 11 76