Vocabulary for Geometry. Line (linea) a straight collection of points extending in opposite directions without end.

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1 Vocabulary for Geometry Line (linea) a straight collection of points extending in opposite directions without end. A line AB or line BA B Symbol for a line is AB Jan 27 2:56 PM Line Segment (linea segmento) is a part of a line. A B C Line segment AB or BC Symbol for a line segment is BC Point Point (punto) an exact position on a line, on a plane, or in space. C Point are always Capital Letters This dot represents point C. Jan 27 3:02 PM 1

2 Ray (rayo) a part of a line that begins at a point and continues without end in one direction. A ray AB The first point is the end point of the ray. B Symbol for a ray is AB Jan 27 3:13 PM Right Angle (angulo recto) an angle that forms a corner and measures 90. It is often marked with a small square. 90 > 90 < 90 Right Angle Obtuse Angle Acute Angle Not Right Angles A right angle is larger than an acute angle and smaller than an obtuse angle. Jan 27 3:23 PM 2

3 Obtuse Angle (angulo obtuso) an angle whose measure is between 90 and 180. An obtuse angle is larger than both a right angle an acute angle. Jan 27 3:33 PM Acute Angle ( angulo agudo) an angle whose measure is between 0 and 90. An acute angle is smaller than both a right angle and an obtuse angle. Jan 28 6:43 AM 3

4 Straight Angle an angle that measures 180 and thus forms a straight line. C Acute A B Obtuse D Angle ABD is a STRAIGHT ANGLE. Angles ABC and CBD are NOT Straight Angles Jan 28 6:34 AM Polygon (poligono) a closed, flat shape with straight sides (3 or more sides). Polygons Not Polygons Jan 28 6:43 AM 4

5 Shape Number of Sides Name of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 8 Octagon Jan 28 6:53 AM Triangles Name Example Description Equilateral Triangle Isosceles Triangle Scalene Triangle All three sides are equal in length, and all angles are equal. At least two of the three sides are equal in length, and two equal angles. All three sides have different lengths, all angles are unequal. Jan 28 7:13 AM 5

6 Name Example Description Acute Triangle All three angles are acute. Right Triangle One angle is a right angle, 90 Obtuse Triangle One angle is an obtuse angle. Jan 28 7:21 AM Quadrilaterals Shape Characteristic Name Trapezium No sides parallel One pair of parallel sides Two pairs of parallel sides Trapezoid Parallelogram Parallelogram with equal sides Parallelogram with right angles Rectangle with equal sides Rhombus Rectangle Square Jan 28 7:28 AM 6

7 Area (area) the size of the inside of a flat shape. Area is measured in square units. 5 in. 2 in. The area of this rectangle is 10 square inches. 10 in 2 Area of a rectangle is; A = L x W Area = Length x Width 5 in. x 2 in. 10 in. 2 Jan 28 8:39 AM Perimeter (perimetro) the distance around a closed shape. 6 in. A A; starting point 4 in. 6 in. 4 in. The perimeter of this rectangle (from point A around to point A) is 20 inches. Perimeter of a rectangle is; P = 2 x (L + W) 2 times length plus width Perimeter is the sum of all sides!!!!!!! Jan 28 8:46 AM 7

8 Find the Area and Perimeter of each rectangle or square. 7 in. 3 in. A = L x W P = 2 x (L + W) Jan 28 8:54 AM 6 mm 6 mm Area of a square is SIDE squared 6 2 = 36 mm 2 or 36 square milimeters Jan 28 8:57 AM 8

9 Area of a Triangle Notice that the area of any triangle is: 1 2 the area of a parallelogram with the same base and height So the formula for the ares of a triangle is: A = 1 2 bh or A = bh 2 The height is perpendicular to the base. 6 cm Area is expressed in SQUARE units (16 cm ) 2 4 cm 8 cm 5 cm 1 2 A = (8cm)(4 cm) 4 x 4 = 16 cm 2 Jan 30 7:20 AM Area = 1 hb Perimeter = S1 + S2 + S cm 10 cm Height 8 cm 14 cm Base Always indicates the HEIGHT and BASE Jan 30 8:16 AM 9

10 height 10 cm base 10 cm Jan 30 8:18 AM Area of Complex Shapes Area of a RECTANGLE; A = lw Area of a TRIANGLE; = 1/2(hb) 1. Divide the shape into two or more parts. 2. Find the area of each part. 3. Add the parts. 8 cm 6 cm 10 cm? cm? cm 3 cm 4. Sometimes it is easier to make a bigger rectangle and subtract a small part to find the area. Feb 2 8:33 AM 10

11 9 cm 5 cm Find the Area: Perimeter: 3 cm 9 cm Feb 2 7:28 AM 15 cm 8 cm 10 cm Feb 2 8:23 AM 11

12 2 cm 9 cm 4 cm 2 cm 4 cm 12 cm Feb 2 8:58 AM Perimeter of Complex Shapes Perimeter means to add all the sides. * Some sides will not be labeled. * Add or Subtract as needed to find the length of those sides that are missing. * Hint: Sometimes it helps to use two different colors. Trace over all horizontal lines in one color. Trace over all vertical lines in another color. Example: 8 in. 4 in. 2 in. 10 in. Add the lengths of all the sides to find the perimeter 8 in. + 4 in. + 6 in. + 6 in. + 2 in in. = 36 in = m 6 in. = m 8-2 = n 6 in = n Feb 4 8:18 AM 12

13 7 in. 6 in. 2 in. 10 in. Hint: subtract when you have the largest side!!! Feb 4 9:39 AM 4 m 8 m 4 m 3 m Hint: Add when the largest side is missing!!! Feb 4 10:00 AM 13

14 8 ft. 8 ft. Area = 64 ft 2 Perimeter = 32 ft. 8 ft. 8 ft. Feb 5 8:18 AM Parallelogram Area: base times height To find the area, multiply the base by the height. * The height is perpendicular to the base. * Do not be distracted by the slanted side. Example: Find the area of this Parallelogram. 5.2 cm 6 cm Base 5 cm Height A = bh A = (6)(5) A = 30 sq. cm Feb 5 7:02 AM 14

15 Remember, perimeter does not include the height!!!!!!! Area = height x base 4.5 cm 4 cm 6 cm A = P = Feb 5 7:13 AM Area = Height x base 8.5 in. 6 in. 12 in. Area = Perimeter = Feb 5 7:15 AM 15

16 Hint; find missing sides, divide figure into rectangles, add the areas 2 m 4 m 4 m 10 m 12 m Area = Perimeter = Feb 5 8:05 AM Feb 6 9:04 AM 16