Post on 24-Dec-2015
Math 1 March 15th
WARM-UP: QUIZ TODAY!!In a triangle…1. The three altitudes intersect at the ____________.2. The three angle bisectors intersect at the __________.3. The three medians intersect at the ____________.4. The three perpendicular bisectors intersect at the ____.5. S is the centroid in the triangle below.
SV = 4, UW = 5, and QW = 21Find the measure of:a) STb) TWc) QS
Announcement for Freshman:
• You must pass your MATH class and your ENGLISH class to be promoted to 10th grade.
• So, if you fail MATH OR ENGLISH, you will stay in 9th grade next year.
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