4) Find the value of the variable and YZ if Y is between X and Z. XY = 2c +1, YZ = 6c, XZ = 9c 1 6(2) 12 YZ YZ

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1 Pre-AP Geometry 1 st Semester Exam Study Guide 1) Name the intersection of plane DAG and plane ABD. (left side and back) AD ) Name the intersection of HI and FJ E 3) Describe the relationship between the lines: A) DC and FE parallel B) GH and BC skew C) HE and EC intersecting 4) Find the value of the variable and YZ if Y is between X and Z. XY = c +1, YZ = 6c, XZ = 9c 1 XY YZ XZ c 1 6c 9c c 1 c c YZ YZ YZ 6c 6() 1 5) Find the coordinates of T given that M is the midpoint of KT. K(10, -) M(, -1) OR x10 y (, 1), x10 y 1 4 x10 4 y 6 x y

2 6) Find ma if ma is 30 less than times its supplement. m A(supp) 30 x (180 x) 30 x 360 x30 3x 330 x 110 m A 110 OR m A x 30 supp x x 30 x180 3x 10 x 70 m A ( ) 3 0 m A 7) Write the equation of a line, in slope-intercept form that passes through (1, 4) and has a slope of -. y y y ( x1) 4 x 4 x 8) Write an equation in point-slope form parallel to y = 3x + and passes through (6, 5). Parallel lines have the same slope. Slope of y = 3x + is 3, so slope of line parallel is also 3. y 3( x 6) 5 9) Describe the relationship between the line that passes through (6, 8) and (, 11) and the line that passes through (1, 3) and ( 3, 6). Slope for (6, 8) and (, 11) Slope for (1, 3) and ( 3, 6) m 6 4 m Slopes are the same therefore the lines are parallel.

3 Give the slope and y-intercept and graph the line. 10) y = 4x 1 11) x + 3y = 6 m = 4, b = -1 A m C 6 b B 3 B 3 1) y = x 13) x = 14) y = 4 Or y1x 0 m = 1, b = 0 Vertical line Slope = undefined No y -intercept Or y0x 4 m = 0, b = 4 horizonal line

4 15) Determine the next item in the sequence. A) 1,, 4, 7, 11, 16 (add 1, add, add 3, add 4, so add 5) B), 4, 8, 16, 3 ( multiply by -) C) 3, 8,, ½, ⅛ (divide by 4 or multiply by ¼ ) 16) Make a conjecture about each value or geometric relationship. A) 1 and are vertical angles 1 (vertical angle thm) B) 3 and 4 are a linear pair 3supp 4 (linear pair post.) #17 and #18: Find a counterexample. 17) If a number is divisible by 10, then it is divisible by 0. One example: 30 is divisible by 10, but not by 0. 18) The quotient of two whole numbers is always a whole number. One example: 5 divided by 8 is not a whole number. Find the converse, inverse, & contrapositive. 19) If it is payday, then I will get ice cream. Converse: If I will get ice cream, then it is payday. Inverse: If it is not payday, then I will not get ice cream. Contrapositive: If I will not get ice cream, then it is not payday.

5 Determine if the final statement is a valid conjecture. If so, write valid. If not, write invalid. 0) If you have a part time job, you work 0 hours a week. Joey has a part time job. Joey works 0 hours a week. Valid by law of detachment 1) If you have a part time job, then you work 0 hours a wk. If you work 0 hours a wk, then you will fall asleep in class. Monica has a part-time job Monica will fall asleep in class. Valid by law of syllogism ) Make a truth table for: p ( q p) p q p ( q p) p ( q p) T T F T F T F F T F F T T T T F F T F F Using the given statements, determine what property is used for the final statement 3) 1. 7(x 3) = = 7(x 3) symmetric 4) 1. If x + 19 = 7.. x = 8 Subtraction property 5) 1. 1 = x + 8. x + 8 = 3y 3. 1 = 3y Transitive or substituion

6 Find the measure of each numbered angle. 6) m1 = x, m = x m 1m 90 x x 6 90 x 96 x 48 m 1 48, m m ) m7 = 3x - 15, m5 = x m 7 m 5 ( vert. angles) 3x15 x x 15 m 7 3(15) m 5 (15) 30 m 6 m ) m4 = 3(x 1), m5 = x m 4 m ( linear pair) 3( x1) x x 3 x x x 176 x 44 m 4 3(44 1) 19 m

7 Write a two-column proof 9) Given: ABC and DBE are vertical angles. Prove: x = 15 STATEMENTS REASONS 1) Given ) ABC DBE Vertical angle theorem 3) m ABC m DBE Def of 5x x + 0 4) 5x 10 = 3x + 0 Substitution 5) x 10 = 0 Subtraction property 6) x = 30 Addition property 7) x = 15 Division property A D B C E 30) Given: B is the midpoint of AC C is the midpoint of BD Prove: AB CD Statements Reasons 1) Given ) AB BC. BC CD Def. of midpoint 3) AB CD transitive Describe the relationship: 31) 1 and 1 alt. exterior 3) 3 and 6 same side int. 33) 4 and 10 alt. interior 34) 1 and 8 alt. exterior 35) 5 and 7 vertical angles 36) 3 and 4 linear pair angles

8 Find the value of x that will allow you to prove JK // LM 37) 38) (3x 13) J K 130 L M J L 87 (x + 9) K M 3x x x 63 x 1 x 9 87 x 58 x 9 39)Classify ABC by the length of its sides if AB = 8, BC = 8, and AC = 10. sides are congruent, therefore isosceles 40) Classify the triangle with angles measuring 97, 63, and 0. one angle is greater than 90, therefore obtuse. 41) Two sides of a triangle have sides 6 and 18. Find the range of the length of the third side = 1 and = 4 therefore 1 < x < 4 4) What is the measure of angle x? x 59 x x 31 or x x 149 x 31

9 43) Find the values of x and y. (angles across from sides are ) y y x y180 (78) x x 180 x 4 y 44) Complete the congruence statement. EFG HIJ 45) Find the value of x and m if RL is an altitude of RTU, m1 = 6x 3 and m = 7x + since RL is an altitude, then RT m 1m 90 6x 3 7x 90 13x x 91 x 7 m 7( 7) 51 TU 46) If RS in an angle bisector of RTU, and murs = x 5 and mtrs = x + 15, find the value of x and murt. m URS m TRS x 5 x15 x 0 m URT ( m TRS) m URT (0 15) 70

10 47) Find the value of x. x 3 x x 64 x ) Find the value of x. 9x - 7 4x + 8 6x + Since angles are congruent, then sides are congruent. So 9x-7 = 4x+8 = 6x+. Just use any two of these. 4x 8 6x 8 x 6 3 x x 49) Are the triangles congruent? If so, state theorem used. No, you only know about one pair of angles and the shared side. 50) Are the triangles congruent? If so, state theorem used. Yes, by HL

11 51)Given: AD CD; BD bisects ADC Prove: ΔABD ΔCBD B A C D Statements Reasons S 1) Given A ) ADB CDB Def. of angle bisect S 3) BD BD Reflexive 4) ΔABD ΔCBD SAS 5) Given: EH bisects DG, D G Prove: ΔDEF ΔGHF Statements Reasons A 1) Given S ) DF FG Def of bisect A 3) DFE HFG Vertical angle thm 4) ΔDEF ΔGHF ASA 53) In DFE, FK is a median, FJ is an angle bisector, and HF is an altitude. a) Name right angles: DHF, EHF b) Name congruent (non-right) angles: DFJ EFJ c) Name congruent segments: DK EK

12 54) If R is the circumcenter of ABC, find the value of x, y, and z. RC=RA=RB (circumcenter is same distance from each vertex) Circumcenter is POC of bisectors so line j goes through the midpoint of CA 3z z 51 z 17 4x x 8 x 7 8y 4 1 8y 16 y 55) C is the centroid of JLM (centroid is /3 distance from vertex to midpt) A) CZ = 3 Find JC and JZ JC ( CZ) JC 6 JZ B) MC = 8. Find CY and MY C) LX = 4. Find CX and CL 1 CY MC CY 4 MY CX LX 3 CX 8 CL ( CX ) 16 56) Name all the angles whose measures are: A) less than 8. 4, 6, 7, B) greater than. 4, 8

13 57) Name the angles from greatest to smallest. Largest angle is across from longest side, smallest angle is across from shortest side. A, C, B 58) Determine the relationship between the given pair of angle or segment measures. (use hinge theorem) A) JM _>_ KL B) mcda _<_ mdab 59) If ms = 5x and mq = 155, find the value of x for which PQRS must be a parallelogram. Opposite angles are congruent P Q m S m Q 5x 155 x 31 S R

14 60) In the parallelogram, find the value of x, AB, and BC. Opposite sides are congruent AB DC 4x10 x x 10 x 5 AB 4(5) BC AD (5 ) 4 6 x 4 D A x 4x 10 C B 61) For parallelogram ABCD, AC = 40, AG = x + 4, DG = 4y 10, GB = y + 5. Find x and y. Diagonals bisect each other. AC ( AG) DG GB 40 (x 4) 4y 10 y x 8 3 4x x 3 15 y y 5 8 A G D C B 6) Find the sum of the interior angles of a convex 15-gon. Sum of interior angles = (n-)180 S (15 )180 S (13)180 S 340

15 63) Find the measure of an interior angle of a regular dodecagon. int ( n )180 n int (1 )180 1 int int 150 OR ext 30 n 1 int 180 ext int ) What do these symbols mean? a. congruent b. AB segment with endpoints of A and B c. AB line through points A and B d. AB ray with starting point at A and going through point B e. A angle with vertex at A f. m A measure of angle with vertex at A g. perpendicular h. ABC triangle with vertices A, B, and C j. a//b line a parallel to line b