Geometry Basically, Geometry is the study of shapes and is one of the oldest branches of mathematicS
The Elements Point is that which has no (Straight) Line is a line that lies evenly with the Plane (Surface) is a plane that lies evenly with part points on itself the straight lines on itself
Basic Terms & Definitions D A ray starts at a point (called the endpoint) and extends indefinitely in one direction AB A B A line segment is part of a line and has two endpoints. AB A B
0 An angle is formed by two rays with the same endpoint. sid verte sid An angle is measured in degrees The angle formed by a circle has a measure of 360 degrees.
A right angle has a measure of 90 degrees. A straight angle has a measure of 180 degrees.
0 A simple closed curve is a curve that we can trace without going over any point more than once while beginning and ending at the same point. A polygon is a simple closed curve composed of at least three line segments, called sides. The point at which two sides meet is called a vertex A regular polygon is a polygon with sides of equal length.
Polygons No of sides name of Polygo triangle quadrilateral pentagorn hexagon heptagor octagon nongorn decagon 9 10
Quadrilaterals D Recall: a quadrilateral is a 4-sided polygon. We can further classify quadrilaterals: A trapezoid is a quadrilateral with at least one pair of parallel sides. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A kite is a quadrilateral in which two pairs of adjacent sides are congruent. A rhombus is a quadrilateral in which all sides are congruent. A rectangle is a quadrilateral in which all angles are congruent (90 degrees) A square is a quadrilateral in which all four sides are congruent and all four angles are congruent.
General to Specific Quadrilater trapezoi kite parallelogra rhombus rectangle square
Perimeter and Area 0 The perimeter of a plane geometric figure is a measure of the distance around the figure. The area of a plane geometric figure is the amount of surface in a region 0 area perimeter
Parallelogram Perimeter 2a 2b Area hb Area of a parallelogram- area of rectangle with width - h and length b
Ex: What is the perimeter of a triangle with sides of lengths 1.5 cm, 3.4 cm, and 2.7 cm? 1.5 2.7Perimeterab + C - 1.5 2.7 3.4
Ex: A parallelogram has a based of length 3.4 cm. The height measures 5.2 cm. What is the area of the paralle ramrea (base) Areaht (3.4)(5.2) - 17.86 cm2 5.2 3.4
Ex: The width of a rectangle is 12 ft. If the area is 312 ft2, what is the length of the rectangle? Area = (Length) (widEat L = Length 312 312 (L) (12)26 ft Check: Area= (Length)(width) (12)(26)
Circle I A circle is a plane figure in which all points are d The radius, r, is a line segment from the I The diameter, d, is the line segment across D The circumference, C, of a circle is the  The area of a circle is A = Tr. equidistance from the center. center of the circle to any point on the circle the circle through the center. d = 2r distance around the circle. C 2nr
Ex: Composite Figure
Ex: Find the perimeter of the following composite figure 4 8 0 4 60 a 42 a- P imeter 286o 12 42 + b a 28 b 12 b- - 28 + 60 + 12 42+ 16 + 18
Ex: Find the area of the figure 4 4 3.5 3.5 Area of rectangle = (4)(35) 14 The area of the figure 4 area of rectangle-cut out area = 14-2 square units. Diameter = 4 radius-2 Area of circle = 2? = 4 Area of half the circle 2 (4r)
Ex: A walkway 2 m wide surrounds a rectangular plot of grass. The plot is 30 m long and 20 m wide. What is the area of the walkway? What are the dimensions of the 2 big rectangle (grass and walkwaMath = 2 + 20 + 2 = 0 2 24 Thee bgtelahgle has area (24)(34) 816 m2 What are the dimensions of the small rectangle 20 by 30 tyre SMall rectangle has area (20)(30) 600 Th area of the walkway is the difference between the big and small rectangl A rea 816-600 216 m2
Find the area of the shaded region 1 0 Area of square 102 = 100 Area of each circle = 52 = 25 of the circle cuts into the square. But we have four 4 4(%)(25) cuts into the area of the 5 1 Therefore, the area of the shaded reninn = area of squa circles = 100-25 square units
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