ABC. GEOMETRY SEMESTER ONE REVIEW SHEET PART I: Fill in the Blanks Given: is the midpoint of BE, , AB EC, BC XY , X. is the midpoint of EC.

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1 GEOMETRY SEMESTER ONE REVIEW SHEET PRT I: Fill in the Blanks Given: l Y m, B EC, BC XY is the midpoint of EC, X is the midpoint of BE, 0 B 3 X E l ) If BC is equilateral, then m5 7 Y ) If m6 50, then m4 3) If B BC, and m4 0, then m C 4 m 4) If m9 30, then m 5) If B C, and m5 80, then m 6) If m4 0, then m 7) If m4 (5x 5) and m (5x5), then 8) If m8 (x 40) and m (3x 0), then m0 m7 9) If B BC, m 30, then m3 0) If BE, then XE ) If BC bisects BE, m5 40, then m5 ) If m4 (5x ), m (3x), and m (x6), then x 3) m3 m3 m7 m6 4) Find the sum of the measures of the angles of the polygon BXYC 5) If B 4x 0 and CE x 48, then x 6) If m3 80, then m5 7) If m6 5, then m3 8) If m4 5, and m 50, then m 9) The total number of diagonals than can be drawn in polygon BXYC is 0) raw CX CX is called a of BEC ) If m (5x ), m3 6x, and m4 (6x 8), then m3 ) If m (7x), and m7 (9x), then m6 3) If m5 88, then m6 4) If XY YE, and m5 58, then m8 5) If m7 4 and B C, then m

2 PRT II: lways/sometimes/never, True/False, and Multiple Choice Complete each statement with the word always, sometimes, or never 6) When there is a transversal of two lines, the three lines are coplanar (Look up definition of transversal) 7) Three lines intersecting in one point are coplanar 8) Two lines that are not coplanar intersect 9) Two lines parallel to a third line are parallel to each other 30) Two lines skew to a third line are skew to each other 3) Two lines perpendicular to a third line are perpendicular to each other 3) Two planes parallel to the same line are parallel to each other 33) Two planes parallel to the same plane are parallel to each other 34) Lines in two parallel planes are parallel to each other 35) Two lines parallel to the same plane are parallel to each other 36) Two lines that do not intersect are parallel 37) Two skew lines intersect 38) Two lines parallel to a third line are skew 39) If a line is parallel to plane X and also to plane Y, then plane X and plane Y are parallel 40) Plane X parallel to n is parallel to plane Y If plane Z intersects X in line k and Y in line n, then k is 4) If a triangle is isosceles, then it is equilateral 4) If a triangle is equilateral, then it is isosceles 43) If a triangle is scalene, then it is isosceles 44) If a triangle is obtuse, then it is isosceles Complete each statement with the word true or false 45) Three given points are always coplanar 46) Each interior angle of a regular n gon 47) If RST RSV, then SRT SRV has measure ( n )80 n 48) If a quadrilateral has one pair of consecutive supplementary angles, then it is a parallelogram 49) If all the sides of a parallelogram are congruent then it is regular

3 Multiple Choice Problems from Textbook 50) Page 66 # - all 5) Page 67 # all 5) Page 68 # 9 all,, 53) Page 69 # - 4 all 54) Page 630 # - all PRT III: Proofs 55) Given: G FE GP and, GP EO EOF Prove: GP EOF 3 P E, are right angles F 4 56) Given: Quad NRSM is a parallelogram, Prove: G O 4 5 GRM a parallelogram 58) Given: M Prove: G H 4 is the midpoint of GH, 3 G K M 4 3 J H 59) Given: B is a median of CB CE E Prove: E is an angle bisector of CE 57) Given: j k, 4 0 Prove: l m j l 7 m ) Given:, 3 4 Prove: XC is isosceles B 3 4 X k C

4 , 6) Given: PU SR Prove: Q T Q, RQ UT 6) Given: and E BC BC Prove: C CE are midpoints, B P U R S E T C PRT IV: lgebraic Problems 63) If m 5x, m (7x ), and mob (x 4), then x O C B 64) If m (x 8) and m (3x4), then 3 m 3 65) The measure of the supplement of an angle is four times the measure of its complement Find the measure of the angle 66) If and measure of each angle are the acute angles of a right triangle, and m (30 x) and m (40 x), find the

5 a b Given:, c d 67) If m ( x) and m (4x), then m3 c a 3 4 b d 5 6 Given: a b, c d 68) If m4 (x08) and m x x, then m5 6 ( ) c a 3 4 b d ) If m (6x0), m (x 4), and m3 ( x 4), then m ) If m (7x 4), m (x 4), and m4 (50x 48), then m ) The number of diagonals from a single vertex in a regular polygon is Find the measure of each interior angle of the polygon

6 7) If each of 4 interior angles of a convex pentagon has a measure of 05, find the measure of the fifth interior angle 73) Find the total number of diagonals that can be drawn in a regular polygon if each interior angle has measure 35 B 74) Polygon BCE is regular Find m C E 75) BC is isosceles with B C find the measure of the vertex angle If m (0x 8 y), mb ( x y), and mc (4x 5 y), 76) EF is equilateral Find x and y if m (0x 4y 4) and me (x 9y 0) Given: Quad SOPH is a parallelogram S O 77) If SH, then OP 78) If msop 76 and msho 3, then mohp H P 79) If msop (8x 30) and mshp (0x 0), then x Given: mem 30 Find the indicated measures 80) mf 83) mmr 8) mf 8) mmr 84) me 85) mr F E M R

7 86) State whether a given quadrilateral BC is a rectangle, rhombus, square, trapezoid or an isosceles trapezoid () BC, BC, C B () C B, B C, BC, C B (B) BC, B C (E) C, mc 90, BC (C) BC, B, B C (F) B C, C B GEOMETRY SEMESTER ONE REVIEW SHEET - NSWERS PRT I: Fill in the Blanks ) 60º ) 50º 3) 40º 4) 50º 5) 50º 6) 70º 7) 85º 8) 00º 9) 75º 0) ) 70º ) 7 0 3) 360º 4) 540º 5) 4 6) 80º 7) 55º 8) 75º 9) 5 0) median ) 5º ) 83º 3) 88º 4) 64º 5) 7º PRT II: lways/sometimes/never, True/False, and Multiple Choice 6) 7) S 8) N 9) 30) S 3) S 3) S 33) 34) S 35) S 36) S 37) N 38) N 39) S 40) 4) S 4) 43) N 44) S 45) T 46) T 47) T 48) F 49) F 50) Pg 66 () B () (3) B (4) (5) (6) B (7) (8) C (9) (0) B () 5) Pg 67 () C () (3) B (4) (5) (6) (7) B (8) B (9) (0) B () 5) Pg 68 () () (3) B (4) (5) (6) B (7) (8) C (9) () C () 53) Pg 69 () S or S () S (3) S or S (4) HL (5) SSS (6) S (7) SS (8) HL (9) (0) () () C (3) B (4) C 54) Pg 630 () () (3) (4) (5) B (6) B (7) (8) C (9) B (0) C () C () B PRT III: Proofs 55) Statements Reasons ) Given ) G FE, GP EO GP and EOF are right angles ) GP and EOF 3) GP EOF 3) HL are right triangles ) def of rt triangle

8 56) Statements Reasons ) NRSM is a parallelogram, 4 5 ) Given ) NR SM ) def of parallelogram 3) 3 is supp to 7 is supp to 6 4) NRS SMN 4) opp angles of parallelogram are congruent 5) mnrs m SMN 5) ef 6) mnrs m3 m 4 6) P msmn m5 m 6 7) m3 m4 m5 m 6 7) Substitution 8) m4 m 5 8) ef 9) m3 m 6 9) Subtraction prop equality 0) ) ) GRM is a parallelogram 3) if, then same-side int s supp 0) ef ) Supplements of congruent angles are congruent ) If both pairs of opposite angles of a quad are congruent, the quad is a parallelogram 57) Statements Reasons ), ) Given j k 4 0 ) 0 ) if,then corrsp s 3) 4 3) subst property 4) l m 4) if corr s, then lines 58) Statements Reasons ) Given ) M is the midpoint of GH, G H, 3 ) GM MH 3) GKM HJM 3) S 4) MK MJ 5) 4 5) ITT ) def of midpoint 4) CPCTC 59) Statements Reasons ) B is a median of CB ) given ) is the midpoint of C ) definition of a median 3) C 3) definition of a midpoint 4) CE E 4) given 5) E E 5) Reflexive Property 6) CE E 6) SSS 7) CE E 7) CPCTC 8) E is an angle bisector of CE 8) definition of an angle bisector

9 60) Statements Reasons ) ) X BX, 3 4 ) Given ) ITT conv 3) X BXC 3) vertical angles are congruent 4) X BXC 4) S 5) X XC 5) CPCTC 6) XC is isosceles 6) def of isosceles triangle 6) Statements Reasons ) Given ) PU SR, ) RU RU, RQ UT ) reflexive 3) PU SR 3) def of 4) PU RU RU SR 4) addition prop 5) PU UR PR, RU RS US 5) SP 6) 7) PR US PR US 6) substitution 7) def of 8) POR STU 8) SS 9) Q T 9) CPCTC 6) Statements Reasons ) & E are midpoints, ) Given BC BC ) C C ) reflexive 3) B, BE EC 3) def of midpoint 4) B, BE EC 4) def of 5) B B, BE EC BC 5) segment addition postulate 6) ITT Conv 6) B BC 7) B BC 7) def of 8) B BE EC 8) substitution 9) EC EC 9) substitution 0) EC ) EC ) EC 3) C CE 3) SS 0) distributive prop ) division prop of = ) def of

10 PRT IV: lgebraic Problems 63) 6 64) 68º 65) 60º m 40 66) º, 67) 70º 68) 90º or 4º 69) 58º 70) 8º 7) 56 7) 0º 73) 0 74) 7º 75) 0º 76) x 8, 77) 78) 44º 79) 5 3 y 6 m 50 º 80) 0º 8) 30º 8) 50º 83) 5º 84) 60º 85) 05º 86) () rectangle (B) isos trap if B C or parallelogram if B C (C) rhombus () square (E) trapezoid if B C or parallelogram if B C (F) isos trap if BC or rectangle if BC