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? ______