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
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Correct Quizzes• Altitudes• Orthocenter• Medians• Centroid• Perpendicular bisectors• Circumcenter• Angle bisectors• Incenter• Incenter• Circumcenter
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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?
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Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
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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.
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More Important Terms
EQUILATERAL - All sides are congruentEQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent
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Polygons are named by listing its vertices consecutively.
A B
E D
CF
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Polygons can be CONCAVE or CONVEX
CONVEX
CONCAVE
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Ex. 3 Classify each polygon as convex or concave.
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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°
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# 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
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If a convex polygon has n sides, then the sum of the measure of the
interior angles is (n – 2)(180°)
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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°
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Two more important terms
Exterior Angles
Interior Angles
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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
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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
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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
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Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
60°
sum of the exterior anglesnumber of sides
3606
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Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
51.4°
sum of the exterior anglesnumber of sides
3607
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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
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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°
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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°
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Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?
n = 12