Unit 4 Review Packet page 1 Part 1 Polygons Review ate: 1) nswer the following questions about a regular decagon. a) How many sides does the polygon have? 10 b) What is the sum of the measures of the interior angles? 1440 c) What is the measure of each interior angles? 144 d) What is the sum of the measures of the exterior angles? 360 e) What is the measure of each exterior angle? 36 f) How many diagonals can be drawn in the polygon? 35 2) Each exterior angle of a regular polygon is 90. nswer each question about the polygon. a) What is the sum of the exterior angles? 360 b) How many sides does the polygon have? 4 c) What is the name of the polygon? Quadrilateral d) What is the sum of the measures of the interior angles? 360 e) What is the measure of each interior angle? 90 f) How many diagonals can be drawn in the polygon? 2 3) The sum of the interior angles of a regular polygon is 540. nswer each question about the polygon. a) How many sides does the polygon have? 5 b) What is the name of the polygon? Pentagon c) What is the measure of each interior angle? 108 d) What is the sum of the measures of the exterior angles? 360 e) What is the measure of each exterior angle? 72 f) How many diagonals can be drawn in the polygon? 5 Part 2 Segments in Triangles - Give the most specific name for each dotted segment. ltitude Perpendicular isector ngle isector Median
Unit 4 Review Packet page 2 ate: Part 3 etermine whether the triangles are congruent. If they are, name the congruent triangles and the postulate or theorem you used. If there is not enough information, write none. Mark your diagrams. ^ K G H L P LM // PN LP // MN F @ HL KF // HJ G is the midpoint of FH KGF @ JGH S or S J M LPN @ NML S N Q X G R S T W Z Y F J H V S is the midpoint of RT FG // JH; FG @ JH None WXY @ Z SSS FGH @ HJF SS // V T S W VT bisects SVW None None @ @ HL
Unit 4 Review Packet page 3 ate: Part 4 - Solve each algebra connection problem. nswer all questions. 1. 2. 2x 3x - 19 6x + 15 104 9x - 9 2x + 3x 19 + 104 = 180 5x = 95 x = 19 6x + 15 = 9x 9 24 = 3x x = 8 lassify the by its sides: Isosceles lassify the by its angles: Obtuse x = 19 m = 38 m = 38 lassify the triangle by its sides: Isosceles What two sides are congruent? = What two angles are congruent? m = m x = 8 m = 63 m = 63 m = 54 3. 4. 102 48 15x - 30 10x 3x + 42 m = 30 re any of the angles congruent? No Therefore, are any of the sides congruent? No lassify the triangle by its sides: Scalene lassify the triangle by its angles: Obtuse Order the side lengths from longest to shortest: Longest: Middle: Shortest: 15x 30 + 10x + 3x + 42 = 180 28x + 12 = 180 x = 6 x = 6 lassify the by its sides: Equilateral lassify the by its angles: Equiangular m = 60 m = 60 m = 60
Unit 4 Review Packet page 4 ate: NOTE: Many pieces of notation (such as segment bars and rays are missing). 1) is the midpoint of 1) Given 2) = 2) efinition of a Midpoint 3) = 3) Given 4) = 4) Reflexive 5) @ 5) SSS 6) 5 @ 6 6) PT Given: is the midpoint of ; @ Prove: 5 @ 6 5 6 1 2 3 4 1 2 1) is the midpoint of 1) Given 2) = 2) efinition of a Midpoint 3) = 3) Given 4) = 4) Reflexive 5) @ 6) 1 @ 2 5) SSS 6) PT Given: is the midpoint of ; @ 7) bisects 7) efinition of a ngle isector Prove: bisects
Unit 4 Review Packet page 5 ate: Given: @ ; @ 1) = ; = 1) Given 2) = 2) Reflexive 3) @ 3) SSS 4) @ 4) PT Prove: @ Given: @ ; @ 1) = ; @ 1) Given 2) = 2) Reflexive 3) @ 3) SS 4) = 4) PT Prove: @
Unit 4 Review Packet page 6 ate: Given: PR bisects QPS; PQ @ PS Prove: RP bisects QRS 1) PR bisects QPS 1) Given 2) QPR @ SPR 2) efinition of an ngle isector 3) PQ = PS 3) Given 4) PR = PR 4) Reflexive 5) PQR @ PSR 5) SS 6) QRP @ SRP 6) PT 7) RP bisects QRS 7) efinition of an ngle isector Q P R S Given: PR bisects QPS and QRS Prove: RQ @ RS 1) PR bisects QPS 1) Given 2) QPR @ SPR 2) efinition of an ngle isector 3) RP bisects QRS 3) Given 4) QRP @ SRP 4) efinition of an ngle isector 5) PR = PR 5) Reflexive 6) PQR @ PSR 6) S 7) RQ = RS 7) PT P Q R S
Unit 4 Review Packet page 7 ate: Given: // ; // Prove: @ 1) // 1) Given 2) 1 @ 2 2) If lines are parallel, then alternate interior angles are congruent. 3) // 3) Given 4) 3 @ 4 4) If lines are parallel, then alternate interior angles are congruent. 5) = 5) Reflexive 6) @ 6) S 1 4 2 3 Given: JL ^ KM; L is the midpoint of KM Prove: JLK @ JLM 1) JL ^ KM 1) Given 2) 2 and 3 are right angles 2) efinition of Perpendicular Lines 3) m 2 = 90; m 3 = 90 3) efinition of Right ngles 4) m 2 = m 3 4) Substitution 5) L is the midpoint of KM 5) Given 6) KL = ML 6) efinition of a Midpoint 7) JL = JL 7) Reflexive 8) JLK @ JLM 8) SS K J 1 2 3 4 L M
Unit 4 Review Packet page 8 ate: Given: TM @ PR; TM // RP Prove: E is the midpoint of TP 1) TM = PR 1) Given 2) TM // RP 2) Given 3) T @ P; M @ R 3) If lines are parallel, then alternate interior angles are congruent. 4) TEM @ PER 4) S 5) TE = EP 5) PT 6) E is the midpoint of TP 6) efinition of a Midpoint T E R M P Given: & are right angles; @ Prove: @ 1) & are right angles 1) Given 2) = 2) Given 3) = 3) Reflexive 4) @ 4) HL