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Geometry Section 6-1A Exploring Quadrilaterals Pg. 396 You will need your protractor.

Geometry Section 6-1A Exploring Quadrilaterals Pg. 396 You will need your protractor. A quadrilateral is any shape with 4 sides. Pg. 396. A diagonal of a quadrilateral is a line segment whose endpoints are opposite vertices. Pg. 396. WY or YW. XZ or ZX.

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Geometry Section 6-1A Exploring Quadrilaterals Pg. 396 You will need your protractor.

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  1. Geometry Section 6-1A Exploring QuadrilateralsPg. 396You will need your protractor.

  2. A quadrilateral is any shape with 4 sides. Pg.396

  3. A diagonal of a quadrilateral is a line segment whose endpoints are opposite vertices. Pg.396 WY or YW XZ or ZX

  4. To name the quadrilateral, you must list the vertices in order. Try It: a. Name quadrilateral ABCD in 3 other ways. Pg.396 b. Name the diagonals of ABCD. *There is no notation for a quadrilateral, but there is notation for a line segment!

  5. Definitions: Parallelogram: Has exactly 2 pairs of parallel sides. Rectangle: Has 4 right angles. Rhombus: Has 4 @ sides. Pg.396 Square: Has 4 rt. angles AND 4 @ sides. Trapezoid: Has exactly 1 pair of parallel sides. A shape can be more than 1 of the above. For example, a square is also a rhombus, a rectangle and a parallelogram. But a rectangle may not be a square, etc.

  6. Try It: a. Classify the quadrilateral. Rectangle Pg.397 b. Write 3 true statements about this type of quadrilateral in respect to the other types. (Think “all”, “some” or “no”.) All rectangles are quadrilaterals. All rectangles are parallelograms. Some rectangles are squares. No rectangles are trapezoids.

  7. Explore Draw a 4 sided figure on your paper. Use your protractor to measure each of the interior angles. What do they add up to? Did anyone draw a shape with a “dent” in it? Pg.398 Angle-Sum Theorem for Quadrilaterals: The sum of the interior angles of a convex quadrilateral is 360o.

  8. Example Find the measures of the angles of the quadrilateral. x + (x + 40) + 2x + (x + 10) = 360 5x + 50 = 360 Pg.398 5x = 310 x = 62 The angles measure xo, (x+40)o, 2xo and (x+10)o. The angles measure 62o, 102o, 124o and 72o.

  9. Exercises 1. Name quadrilateral WXYZ in three other ways. #1,2 Pg.399 2. Name the diagonals of WXYZ.

  10. Exercises 3. Draw a quadrilateral ABCD with AB@BC. #3,4 Pg.399 4. Draw a quadrilateral with all sides congruent that is not a square.

  11. Exercises 5. Draw a quadrilateral QRST with QR||ST and QT not parallel to RS. #5 Pg.399

  12. Exercises If a quadrilateral is randomly selected from a set of 5 distinct quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid), find the probability of the following: 10. None of the sides are parallel. 0 #10 - 12 Pg.400 11. The quadrilateral is a parallelogram. 4/5 12. All of the sides are congruent. 2/5

  13. Example Find the measures of the angles of the quadrilateral. x + (4x – 100) + (2x + 10) + 3x = 360 10x – 90 = 360 #13 Pg.400 10x = 450 x = 45 The angles measure 45o, 80o, 100o and 135o.

  14. Definition A cross section of a solid is the intersection of the solid and a plane. For example, the cross section produced by passing a plane through a cube as shown is a triangle. Pg.400

  15. Exercises Draw and classify the cross section of the solid shown when it is cut by a plane parallel to rEFG. #17 Pg.400 triangle

  16. Exercises Draw and classify the cross section of the solid shown when it is cut by a plane through F and I perpendicular to EG. #18 Pg.400 Rectangle

  17. Homework: Practice 6-1A

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