Geometry Topics Name: __________________________ Unit 4 Review Packet Date: ___________________________ Section 1 – Identify each as a convex polygon, not convex polygon, or not a polygon. 1) _____________ 2) _____________ 3) _____________ 4) _____________ Section 2 – Identify each as a regular polygon or irregular polygon. 5) _____________ 6) _____________ 7) _____________ 3 120 ° 3 3 120° 120 ° 3 3 120 ° 120 ° 3 Section 3 – Vocabulary Matching – Choose the BEST answer. ______ 1. Convex Polygon A. A six sided polygon. ______ 2. Polygon B. A shape formed by many angles, where each segment must intersect with exactly two other segments. ______ 3. Triangle C. A three sided polygon. ______ 4. Quadrilateral D. An angle that forms a linear pair with an interior angle of a ______ 5. Pentagon polygon. ______ 6. Hexagon E. A seven sided polygon. ______ 7. Heptagon F. A five sided polygon. G. An eight sided polygon. ______ 8. Octagon H. A polygon with all congruent sides and angles. ______ 9. Nonagon I. A segment connecting two nonconsecutive vertices of a polygon. ______ 10. Decagon J. A nine sided polygon. ______ 11. Diagonal K. A four sided polygon. ______ 12. Regular Polygon L. A ten sided polygon. ______ 13. Interior Angle M. An angle that lies on the interior of a convex polygon. ______ 14. Exterior Angle N. A polygon such that no two vertices can be connected by a segment on the exterior of the figure. Geometry Topics Unit 4 Review Packet – page 2 Section 4 – Formulas. Fill in the formulas from your notes packet or from the bottom of this page. 1. Sum of the interior angles of a convex polygon - _______________________________ 2. Sum of the exterior angles of a convex polygon - _______________________________ 3. Number of diagonals in a polygon - __________________________________________ 4. Measure of each interior angle in a convex, regular polygon - ______________________ 5. Measure of each exterior angle in a convex, regular polygon - ______________________ Section 5 - Complete the following chart – Hint: Use the formulas from above. Measure of Measure of Sum of Sum of Number Number each interior each exterior Name of polygon interior exterior of of Sides angle if it was a angle if it was a angles angles. Diagonals regular polygon regular polygon 1440° 60° Nonagon 8 4 60° Heptagon 5 180(n − 2) 360 n(n −3) n n-gon 180(n – 2) 360° n n 2 Geometry Topics Unit 4 Review Packet – page 3 Section 6 – Algebra Connections. Solve for the missing variables. 1. 2. x + 12 w z + 57 x 37 2y 3x + 2 2x - 8 w = _______ x = _______ y = _______ x = __________ z = _______ 3. 4. y 115 x 30 60 z 5x x = _______ y 75 y = _______ x = _______ z = _______ y = _______ 5. 6. A B 4x + 13 4x + 25 5x 4x + 17 6x 6x 80 83 D C 4x + 25 4x + 13 x = _______ Is AB || DC? __________ x = _______ Is AD || BC? __________ Geometry Topics Unit 4 Review Packet – page 4 1. ZERO diagonals can be drawn in a given 2. There can be 2 diagonals drawn in a given regular polygon. regular polygon. How many sides does the polygon have? ___________ How many sides does the polygon have? ___________ What is the name of the polygon? What is the name of the polygon? _______________ ________________________________________ What is the sum of the interior angles? __________ What is the sum of the interior angles? __________ What is the measure of each interior angle? _______ What is the measure of each interior angle? _______ What is the sum of the exterior angles? __________ What is the sum of the exterior angles? __________ What is the measure of each exterior angle? ______ What is the measure of each exterior angle? ______ 3. The measure of each interior angle of a 4. The measure of each interior angle of a regular polygon is 144°. regular polygon is 60°. What is the sum of the interior angles? __________ What is the sum of the interior angles? __________ How many sides does the polygon have? ___________ How many sides does the polygon have? ___________ What is the name of the polygon? What is the name of the polygon? ________________________________________ ________________________________________ What is the sum of the exterior angles? __________ What is the sum of the exterior angles? __________ What is the measure of each exterior angle? ______ What is the measure of each exterior angle? ______ How many diagonals can be drawn? ______________ How many diagonals can be drawn? ______________.