Geometry/Trig 2Name: __________________________ Unit 3 Review Packet ANSWERSDate: ___________________________ Section I – Name the five ways to prove that parallel lines exist. 1.If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. (Show 1 pair of corresponding angles are congruent.) 2.If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. (Show 1 pair of alternate interior angles are congruent.) 3.If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel. (Show 1 pair of same side interior angles totals 180) 4.If 2 lines are parallel to the same line, then they are parallel to each other. (Show that both lines are parallel to a third line.) 5.If 2 lines are perpendicular to the same line they are parallel to each other. (Show that both lines are perpendicular to a third line) Section II – Identify the pairs of angles. 1.  1  &  4 ___Vertical angles_____ 2.  3  &  6 ___Alternate Interior Angles_ 3.  8  &  4 ___Corresponding Angles__ 4.  2  &  7 ___Alternate Exterior Angles 5.  3  &  5 __Same Side Interior Angles_ 6.  1  &  6 ___none______________ ) Vertical angles p are ____congruent____ 2.) Angles in a linear air are ____ Supplementary ___________. 3.) If two parallel lines are cut by a transversal, then corresponding angles are ____congruent______. 4.) If two parallel lines are cut by a transversal, then alternate interior angles are ___congruent_____. 5.) If two parallel lines are cut by a transversal, then alternate exterior angles are ___congruent___. 6.) If two parallel lines are cut by a transversal, then same side interior angles are __ Supplementary __. 7.) If two parallel lines are cut by a transversal, then same side exterior angles are ___ Supplementary _. Section III – Fill In 8. If two lines are perpendicular to a third, then the two lines are __parallel_________________. 9. The sum of interior angles of a ____triangle___ is The measure of an exterior  of a triangle is the sum of the two _non-adjacent_ _interior_ _angles.

Geometry/Trig 2Name: __________________________ Unit 3 Review Packet – Page 2Date: ___________________________ Section IV – Determine which lines, if any, are parallel based on the given information. If there are parallel lines, state the reason they are parallel b a 1.) m  1 = m  9___c//d______If Corresponding  s are  the lines are //____ 2.) m  1 = m  4 ___none, because the angles are vertical. 3.) m  12 + m  14 = 180 a//b, If Same side interior  s are supplementary the lines are // 4.) m  1 = m  13_none, angles do not share the same transversal____ 5.) m  7 = m  14c//d;  14  15, vertical  s are   7  15, If Corresponding  s are  the lines are // 6.) m  2 = m  11c//d, If alternate interior  s are , the lines are // 7.) m  15 + m  16 = 180_none, linear pair__________ _________________________ 8.) m  4 = m  5 a//b, If alternate interior  s are , the lines are // dc

Section V – Name the following polygons – For triangles name each by side and angles; for all other polygons name whether each is irregular or regular, convex or not convex, and give its name based on the number of sides. Geometry/Trig 2Name: __________________________ Unit 3 Review Packet – Page 3Date: ___________________________ square Triangle, scalene right Pentagon, convex, regular Pentagon, concave, irregular Triangle, acute equilateral, (equiangular) Triangle, isosceles, obtuse Quadrilateral, regular, convex Heptagon, concave, irregular Triangle, scalene acute

Number of Sides Name of polygon Sum of interior angles. Measure of each interior angle if it was a regular polygon Sum of exterior angles. 4Quadrilateral360°90°360° 8Octagon1080°135°360° 10Decagon1440°144°360° 3Triangle180°60°360° 5Pentagon540°108°360° 7Heptagon900°128.5°360° 6Hexagon720°120°360° Section VI – Fill In the Chart Section VII– Find the slope of each line. (Change the equations into slope intercept form.) Determine which lines are parallel and which lines are perpendicular. Line a 8x – 2y = 10y=4x-5, m=4Line b 4y = 6x y=3/2x, m=3/2 Line c 2x - 3y = 9 y=-2/3x-3, m=-2/3Line d y = xm=1 Line e x + y = 2y=-x+2, m=-1Line f 5x – 4y = 4 y=5/4x-1, m=5/4 Parallel lines _____d//e__________ Perpendicular lines ___b  c______ ________________

Section X - Proofs StatementsReasons J GK I H Given: GK bisects  JGI m  H = m  2 Prove: GK // HI 1. GK bisects  JGI 2.  1  2 3.  H  2 4.  1  H 5. BD // EF 1. Given Geometry/Trig 2Name: __________________________ Unit 3 Review Packet – Page 4Date: ___________________________ 2 1 Statements Reasons Given: AJ // CK; m  1 = m  5 Prove: BD // FE AC D E F B JK Given Defn of  bisector Substitution prop of = If corresponding  s are , then the lines are // 1. AJ // CK1. Given 5. GK // HI 2. If 2 lines are //, then alt int  s are  3.  1  5 2.  1  4 4.  4  5 5. If alt int  s are , then the lines are // 3. Given 4. Substitution pro of =