math 1 march 13 th warm-up: 1.which point of concurrency would be equidistant from each road on the...
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Math 1 March 13th
WARM-UP:1. Which point of concurrency would be equidistant from each road on the map?
2. TQ = 5 TS = 12 RU = 6 Find the measures of
these segments:a) TRb) SUc) SV
Main
Stre
et
1st Avenue
Highway 31
Correct Quizzes• Altitudes• Orthocenter• Medians• Centroid• Perpendicular bisectors• Circumcenter• Angle bisectors• Incenter• Incenter• Circumcenter
What does the word “polygon” mean?
What is the smallest number of sides a polygon can have?
What is the largest number of sides a polygon can have?
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
F
A B
C
DE
Important TermsA VERTEX is the point of intersection of two sides
A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL.
CONSECUTIVE VERTICES are two endpoints of any side.
Sides that share a vertex are called CONSECUTIVE SIDES.
More Important Terms
EQUILATERAL - All sides are congruentEQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent
Polygons are named by listing its vertices consecutively.
A B
E D
CF
Polygons can be CONCAVE or CONVEX
CONVEX
CONCAVE
Ex. 3 Classify each polygon as convex or concave.
What is the sum of the measures of the interior angles of a triangle?
180°180°
What is the sum of the measures of the interior angles of any
quadrilateral?
REVIEW:
180°
360°
# of sides
# of triangles
Sum of measures of
interior angles
3 1 1(180) = 180
4 2 2(180) = 360
5 3 3(180) = 540
6 4 4(180) = 720
n n-2 (n-2) 180
If a convex polygon has n sides, then the sum of the measure of the
interior angles is (n – 2)(180°)
Ex. 1 Use the regular pentagon to answer the questions.
A)Find the sum of the measures of the interior angles.
B)Find the measure of ONE interior angle
540°
108°
Two more important terms
Exterior Angles
Interior Angles
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
2
3
4
5
m m m m m 1 2 3 4 5 360
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
3
2
m m m 1 2 3 360
If any convex polygon, the sum of the measures of the
exterior angles, one at each vertex, is 360°.
1
3
2
4
m m m m 1 2 3 4 360
Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
60°
sum of the exterior anglesnumber of sides
3606
Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
51.4°
sum of the exterior anglesnumber of sides
3607
Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?
n = 20
angleexterior sides ofnumber
anglesexterior theof sum
18360
n
Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle?
185°
Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.
30°, 90°, 150°, and 90°
Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?
n = 12