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Geometry/Trig 2 Name: __________________________

Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet ANSWERS Date: ___________________________. Section I – Name the five ways to prove that parallel lines exist.

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Geometry/Trig 2 Name: __________________________

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  1. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet ANSWERS Date: ___________________________ • Section I – Name the five ways to prove that parallel lines exist. • 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.) • 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.) • 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) • 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.) • 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. Ð1& Ð4 ___Vertical angles_____ 2. Ð3& Ð6 ___Alternate Interior Angles_ 3. Ð8& Ð4 ___Corresponding Angles__ 4. Ð2& Ð7 ___Alternate Exterior Angles 5. Ð3& Ð5 __Same Side Interior Angles_ 6. Ð1& Ð6 ___none______________ 1 2 3 4 6 5 8 7 Section III – Fill In • 1.) Vertical anglesp 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_. 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 180. 10. The measure of an exterior Ð of a triangle is the sum of the two _non-adjacent_ _interior_ _angles.

  2. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 2 Date: ___________________________ 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. 1.) mÐ1 = mÐ9 ___c//d______If Corresponding s are  the lines are //____ 2.) mÐ1 = mÐ4 ___none, because the angles are vertical. 3.) mÐ12 + mÐ14 = 180 a//b, If Same side interior s are supplementary the lines are // 4.) mÐ1 = mÐ13 _none, angles do not share the same transversal____ 5.) mÐ7 = mÐ14 c//d; 1415, vertical  s are  715 , If Corresponding s are  the lines are // 6.) mÐ2 = mÐ11 c//d, If alternate interior s are , the lines are // 7.) mÐ15 + mÐ16 = 180 _none, linear pair__________ _________________________ 8.) mÐ4 = mÐ5 a//b, If alternate interior s are , the lines are // 1 2 9 10 a 3 4 11 12 5 6 13 14 b 7 8 15 16 c d

  3. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 3 Date: ___________________________ 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. 1. 2. Pentagon, convex, regular Triangle, scalene right 5 3 4 3. 4. Triangle, acute equilateral, (equiangular) 60 Pentagon, concave, irregular 60 60 5. 6. Triangle, isosceles, obtuse Quadrilateral, regular, convex 8 5 5 square 7. 8. Heptagon, concave, irregular Triangle, scalene acute 9 7 8

  4. 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 = 10 y=4x-5, m=4 Line b 4y = 6x y=3/2x, m=3/2 Line c 2x - 3y = 9 y=-2/3x-3, m=-2/3 Line d y = x m=1 Line e x + y = 2 y=-x+2, m=-1 Line f 5x – 4y = 4 y=5/4x-1, m=5/4 Parallel lines _____d//e__________ Perpendicular lines ___bc______ ________________

  5. Geometry/Trig 2 Name: __________________________ Unit 3 Review Packet – Page 4 Date: ___________________________ Section X - Proofs Given: GK bisects ÐJGI mÐH = mÐ2 Prove: GK // HI J 1 G K 2 Statements Reasons 1. GK bisects JGI 1. Given 2. 1  2 2. Defn of  bisector I H 3. H  2 Given 3. 4. 1  H Substitution prop of = 4. 5. GK // HI If corresponding s are , then the lines are // 5. Given: AJ // CK; mÐ1 = mÐ5 Prove: BD // FE Reasons Statements 1. AJ // CK 1. Given 2. If 2 lines are //, then alt int s are  2. 1  4 3. 1  5 3. Given A C 4. Substitution pro of = 4. 4  5 5. BD // EF 5. If alt int s are , then the lines are // 1 2 3 B D 4 5 F E J K

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