bell work 3/4/13 find the measure of x in each triangle 1) use special right triangles to solve a)b)...
TRANSCRIPT
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
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.
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?
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