Bell Work 3/4/13 Find the measure of x in each triangle 1) Use Special Right Triangles to solve a)b) 2)Use Trig Ratios to solve for the missing side a)b)

Bell Work 3/4/13• Find the measure of x in each triangle• 1) Use Special Right Triangles to solve• a) b)

• 2)Use Trig Ratios to solve for the missing side• a) b)

Outcomes

• I will be able to:• 1) Use properties of special right triangles• 2) Define and name a polygon

• 3) Determine if a polygon is convex or concave

• 4) Determine the measure of all the angles inside a quadrilateral

6.1 Polygons

sides

vertex vertices

ABCDE or DCBAE

Example 1• State whether the figure is a polygon

Names of PolygonsTriangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

N-gon

Types of Polygons• Convex: A polygon in which no line that

contains a side includes a point inside the polygon. (In other words, extend the sides of the polygon. If it crosses inside the polygon, it is not convex!)

• Example:

• Concave: A polygon that is not convex. (Notice it caves in!)

• Example:

On Your OWN-Try Examples 1-3• 1) Draw a convex polygon

• 2) Draw a concave polygon

ConvexQuadrilateral

ConcavePentagon

Types of Polygons• Equilateral Polygon: A polygon with

all sides congruent.

• Equiangular Polygon: A polygon with

all angles congruent.

• Regular Polygon: A polygon with

both equilateral and equiangular.

Examples

No, equilateral only

No, equiangular only

Diagonal

• Example: Draw all of the diagonals for this hexagon

non-consecutive vertices

Quadrilateral Sum

360°

Angle1 + Angle2 + Angle3 + Angle4 = 360

x + 55 + x + 55 = 360

2x + 110 = 360 -110 -110

2x = 250x = 125

Quadrilateral Sum

x + x – 20 + x + 80 = 360

x = 100

No, because not all the angles are the same

Is it regular?

On Your OWN Try Example 3

• 3) Solve for x

x = 20

Parallelograms• Parallelogram: A quadrilateral with both

pairs of opposite sides parallel

• ***Arrows must be present to indicate that the lines are parallel

Theorems about parallelograms• If a quadrilateral is a parallelogram then it is:

Congruent

PS congruent to QR andPQ congruent to SR

Theorems about Parallelograms

Congruent

<P and <R are congruent<S and <Q are congruent

Theorems about Parallelograms

supplementary

P + S = 180Q + R = 180

and P + Q = 180S + R = 180

Theorems about Parallelograms

bisect each other

PM congruent to MR

and

SM congruent to MQ

Examples

Examples

***Hint: It might help drawing a quadrilateral. Thenlook at the angles.

Examples

Exit Quiz• 1) Using what we know about

quadrilaterals find the value of x

• 2) Using what we know about parallelograms, find the value of x, y, and z