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Geometry. Line. Never ending (NO NOTES) ↔. Line Segment. Has two endpoints (NO NOTES) ●▬●. Point. A place on a line (NO NOTES) ●. Plane. An area with geometric figures Also called a coordinate plane. Ray. Consist of an endpoint and a line Used to create angles →. Angle.
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Line • Never ending • (NO NOTES) • ↔
Line Segment • Has two endpoints • (NO NOTES) • ●▬●
Point • A place on a line • (NO NOTES) • ●
Plane • An area with geometric figures • Also called a coordinate plane
Ray • Consist of an endpoint and a line • Used to create angles • →
Angle • Consist of two rays that meet at a vertex • (NO NOTES) • ∟
Vertex • The point that two rays have in common • Used to form angles and polygons
Acute • An angle less than 90 degrees • Used to classify angles and triangles
Right • An angle that measures exactly 90 degrees • Used to classify angles and triangles
Obtuse • An angle that measures greater than 90 degrees but less than 180 degrees • Used to classify angles and triangles
Triangle • Consist of three angles that when added equals 180 degrees • A= 45, B = 45, C = 90 A + B + C = 180 45 + 45 + 90 = 180 180 = 180
Quadrilateral • Is made of four segments that intersect only at their endpoints • Has four vertices that when added equals 360 degrees
Congruent Segments • Have equal lengths • Used to classify polygons
Congruent Angles • Have equal measures • Used to classify polygons
Straight Angle • An angle that measures exactly 180 degrees • A straight line
Reflex Angle • An angle that measures more than 180 degrees but less than 360 degrees • Pay attention to notation (angle symbol)
Complementary Angles • Two angles that add up to 90 degrees • Calculate by subtracting the given angle from 90
Supplementary Angles • Two angles that add up to 180 degrees • Calculate by subtracting the given angle from 180
Vertical Angles • Angles opposite each other when two straight lines cross • (NO NOTES)
Perpendicular Lines • When two lines meet or cross at a right angle • (NO NOTES)
Parallel Lines • Lines that run side by side and never cross • (NO NOTES)
Transversal Line • A third line that crosses two parallel lines • (NO NOTES)
Equilateral Triangle • Has three equal sides and three equal 60 degree angles • (NO NOTES)
Isosceles Triangle • Has two equal sides and two equal angles called base angles, the third angle is called the vertex angle • (NO NOTES)
Scalene Triangle • Has no equal sides and no equal angles • (NO NOTES)
Right Triangle • An isosceles or scalene triangle that has a 90 degree angle • (NO NOTES)
Similar Triangles • Have the same shape but not necessarily the same size • Differ only in the lengths of their sides • All angles are equal
Corresponding Sides • Sides or angles that have the same relative position • The sides that are opposite the equal angles • The corresponding sides can be written as a proportion
Square • Of a number, is that number multiplied by itself • 6 is the base and 2 is the exponent • 6 is called the factor • 6 x 6 = 36 • 62
Perfect Square • Numbers that have whole numbers as their square roots • (NO NOTES) • Example: 152 = 225
Square Roots • Symbol √ (radical) • Think: What number times itself equals this number? • Example √25 = 5
Hypotenuse • In a right triangle the side opposite the right angle • (NO NOTES)
Pythagorean Theorem • Relationship between the hypotenuse and the two shorter sides • Formula – c2 = a2 + b2
Circle • Figure with all points the same distance from the center • Equals 360 degrees
Radius • From the center of the circle to the side • Symbol – r • Equals ½ of the diameter
Diameter • Distance across the circle, from side to side going through the center • Symbol – d • Equals two times the radius
Circumference • The distance around the circle • Formulas • Radius – C = 2∏r • Diameter – C = ∏d
Pi • Greek letter • ∏ • Approximate value is 3.14 or 22/7
Area • Measure of surface, measured in square units • Formulas • Rectangle – A=lw • Square – A =s2 • Triangle – A = 1/2bh • Circle – A = ∏r2 • A = lw • A=6 * 10 • A = 60 squared units
Volume • Measure of the space taken by a solid object • measured in volume units (cubic) • most common shape is the rectangular solid • Formulas • Rectangular solid V= lwh • Cylinder V = ∏r2h • Example • l=4, h = 2, w= 1 • V=lwh • V=4*2*1 • V=8 cubic inches
Perimeter • Distance around a shape • Formula • Square -- P = 4s • Rectangle -- P = 2l + 2w • Triangle –- P = s + s + s • Example • P=4s • P=4*4 • P=16 inches