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Welcome

Welcome. To. Geometry. •. POINT – exact location in space. LINE – Straight path that extends endlessly in both directions. •. B. AB. A. RAY – Is part of a line. It begins at a point and extends endlessly in one direction. Q. R. T. W. Line Segment QR or QR Or RQ or RQ. D.

uriel-patton
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Welcome

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  1. Welcome To Geometry

  2. • POINT – exact location in space LINE – Straight path that extends endlessly in both directions • B AB A RAY – Is part of a line. It begins at a point and extends endlessly in one direction

  3. Q R T W Line Segment QR or QR Or RQ or RQ D PLANE – A flat surface that extends without end in all directions. A plane is named by three points on the plane that are not on a line LINE SEGMENT – is part of a line between 2 endpoints. The endpoints are used to name the line segment. This plane would be named TDW CONGRUENT LINE SEGMENTS – are equal to each other and have the same length. Tick marks are used to show congruent segments.

  4. ANGLES – 2 rays coming together form a angle T S Vertex – where 2 rays meet Q The angle is always labeled with the vertex in the middle This angle would be labeled TQS

  5. A G I A Right Angle is a 90° angle An acute angle is an angle that is less than 90° B C H D Straight Angle = 180° An obtuse angle is an angle that is larger than 90° and less than 180 E F

  6. IF, line AD is equal to 180° Vertical Angles D 130° B Formed by intersecting lines. Vertical angles are congruent or the same size. And AGB and BGD are supplementary 50° 50° G 130° F A IF AGB is = to 50°, THEN, BGD has to be = to 130° Adjacent Angles Share a vertex and have a common side

  7. Complimentary angles will equal 90° G B Then this one has to be 40° F R T D If this angle is 50° If the angle of RTD is 15° Then the angle of GTR has to be 75° C M

  8. SUPPLEMENTARY ANGLES WILL EQUAL 180° B If ABC is 40° Then BCF has to be 140° A C F If 2 angles are supplementary and one is 65° Then the other one has to be ______?

  9. POLYGONS a closed figure formed by 3 or more line segments. Each line segment meets exactly 2 other sides, one on each end in a common endpoint

  10. Regular Polygons – a polygon in which all side are congruent and all angles are congruent These shapes are polygons but not regular polygons

  11. TRIANGLES The sum of the 3 angles of any triangle equals 180° A3-sided polygon Scalene Equilateral Isosceles 60° 60° 60° 2 sides congruent No sides congruent All sides or angles are congruent

  12. Triangles Classified by Angles Right Acute Obtuse 35° 77° 25° 110° 90° 55° 50° 53° 45° 3 acute angles (No angles larger than 90°) Has one 90° angle 1 angle larger than 90°

  13. Angle Measurements in Triangles The sum of the angles in a triangle always equals 180˚ This angle has to equal 130 ˚ 130 ˚ 25 ˚ 25 ˚ 60˚ 45 ˚ 60˚ X 90 ˚ G X has to equal 60˚ 180 ˚ – 135 ˚ = G G = 45˚

  14. Parallelogram Trapezoid 1 pair of opposite sides parallel Pairs of opposite sides are parallel and congruent All four-sided polygons are Quadrilaterals All 4 angles in a quadrilateral will equal 360° Rectangle with 4 right angles and 4 congruent sides Square Rhombus Parallelogram with 4 congruent sides Parallelogram with 4 right angles Rectangle

  15. End of Day 1

  16. Perimeter is the outside edge measurement of a polygon Length Width Width Plus Length P = L + L + W + W

  17. To find the area of a quadrilateral A = L x W Multiply the length time the width W L Or Base times height A = B x H Height Base

  18. Area of Quadrilaterals A = L x W Width 12 x 4 = 48 cm² 4cm A = LW Length 12 cm 10 x 5 = 50 in ² A = B x H Height 5 in A = BH 10 in Base

  19. Base times the height times ½ Area of a Triangle Height 10 cm Base 8 cm A = B x H x ½ or A = B x H ÷ 2 8 x 10 = 80 80 ÷ 2 = 40 cm²

  20. CIRCUMFERENCE is the outside edge measurement of a circle CIRCUMFERENCE Diameter Diameter is the measurement all the way across the center of the circle

  21. Circumference RADIUS RADIUS is the measurement of HALF the circle

  22. To find the circumference of a circle C = Pi x D Multiply 3.14 or П or Pi OR By The Diameter C = П x D D=8 in OR 3.14 x 8 = 25.98 in C = 3.14 x D

  23. To find circumference of a circle when you have only the radius MULTIPLY the radius times 2 THEN multiply by 3.14 or П Radius = 4 in 4 x 2 = 8 8 x 3.14 = 25.12 in C = R x 2 x 3.14 C = R x 2 x П

  24. A = R x R x 3.14 A = R² x П MULTIPLY the radius times the radius Or R² THEN multiply by 3.14 or П Radius = 4 in 4 x 4 = 16 16 x 3.14 = 50.24 in² AREA Of a circle

  25. Area of a Circle A = R² x  Multiply the radius by the radius or R² OR R = 5 5 x 5 = 25 A= ПR² OR Then multiply by 3.14 OR 25 x 3.14 = 78.5 A = R² x 3.14 A = Pi x R²

  26. Area of a Circle A = (D ÷ 2)² x  If you have the diameter OR D = 10 in 1. Divide the diameter By 2 10 ÷ 2 = 5 5 x 5 = 25 2. Multiply the radius by the radius or R² 25 x 3.14 = 78.5 in² Then multiply by 3.14 A = (D ÷ 2)² x 3.14

  27. Volume Of a Cube Multiply the Base times the height times the width Height Width Base V = B x H x W

  28. Volume Of a Cube Multiply the Base times the height times the width 6 feet 10 feet 8 feet 8 x 10 x 6 = 480 ft³

  29. Volume of a cylinder A = R² x 3.14 surface area Then multiply the height Height Find the surface area of the base So, V = R² x 3.14 x H Base

  30. 4 x 4 = 16 Volume of a cylinder Find the area of the base 16 x 3.14 = 50.24 Then multiply the height 50.24 x 10 = 500.24 cm³ R = 4cm 10 cm Height Base A = R² x 3.14 V = R² x 3.14 x H

  31. Volume of a triangular prism V = B x H x ½ x L or V = B x H ÷ 2 x L Height 6 in Find the area of the triangle Length 20 in 10 in Base Then multiply the length 10 x 6 x ½ = 30 x 20 = 600 in³ 10 x 6 ÷ 2 = 30 x 20 = 1200 = 600 in³

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