Ch 9 8 Interior Exterior Angles of Polygons

Ch 9 -8 Interior & Exterior Angles of Polygons? …with a little review C. N. Colon Geometry

REVIEW: Ch 9 -6 and Ch 9 -7 Proving Triangles Congruent by (AAS, HL)

Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. A B HL C E D A D F B C E F If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

Problem Step 1: Mark the Given Step 2: Mark vertical angles Step 4: List the Parts in the order of the method Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL ) Step 5: Fill in the reasons Step 6: Is there more? Statements Reasons Given AAS Vertical Angle Thm Given AAS Postulate

Step 1: Mark the Given Step 2: Mark reflexive sides Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL ) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Statements Reasons Step 6: Is there more? Given HL Given Reflexive Property HL Postulate

Ch 9 -8 Interior and Exterior Angles of Polygons C. N. Colόn Geometry

POLYGONS

POLYGONS 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 Octagon Quadrilateral Nonagon Pentagon Decagon Hexagon Dodecagon Heptagon EQ: How do I find the measure of an interior & exterior angle of a polygon? n-gon 10/17/2007

POLYGONS Important Terms A VERTEX is the point of intersection of two sides F A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL. A B CONSECUTIVE VERTICES are two endpoints of any side. C E D Sides that share a vertex are called CONSECUTIVE SIDES.

More Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR - All sides and angles are congruent POLYGONS

REVIEW: What is the sum of the measures of the interior angles of a triangle? 180° What is the sum of the measures of the interior angles of any quadrilateral? 360° 10/17/2007

If a convex polygon has n sides, then the sum of the measure of the interior angles is (n-2)(180°) By the way concave is the opposite of convex. A concave polygon has sides that “collapse” inward

Use the regular pentagon to answer the questions. A) Find the sum of the measures of the interior angles. 540° B) Find the measure of ONE interior angle 108°

Two more important terms Interior Angles Exterior Angles

In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 2 1 3 5 4

In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2

Find the measure of ONE exterior angle of a regular hexagon. 60°

Find the measure of ONE exterior angle of a regular heptagon. 51. 4°

The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle? 185°

The measure of the exterior angle of a quadrilateral are x, 3 x, 5 x, and 3 x. Find the measure of each angle. 30°, 90°, 150°, and 90°

The sum of the interior angles of a polygon is 720. Find the number of sides. n=6

HW: p. 371 #4 -20 (mo 4) … tomorrow’s HW is the Ch. 9 Review p. 375 # 1 -25 (all)