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Chapter 7: Quadrilaterals

Chapter 7: Quadrilaterals. By Cam Gillis. Lesson 1: Quadrilaterals. Key Terms : Polygon : Figure made up of coplanar segments, attached at the endpoints Each side intersects exactly two other sides Sides intersect only at their endpoints Figure has at least 3 sides

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Chapter 7: Quadrilaterals

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  1. Chapter 7: Quadrilaterals By Cam Gillis

  2. Lesson 1: Quadrilaterals Key Terms: Polygon: Figure made up of coplanar segments, attached at the endpoints • Each side intersects exactly two other sides • Sides intersect only at their endpoints • Figure has at least 3 sides • No two sides with a common endpoint are collinear

  3. Lesson 1: Quadrilaterals Key Terms (continued): Convex Polygon: A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon Concave Polygon: A polygon such that at least one line containing a side of the polygon contains a point in the interior of the polygon Quadrilateral: Polygon with four sides

  4. Lesson 1: Quadrilaterals Key Terms (continued): Diagonal: The segments in a polygon that connect any nonconsecutive vertices Rectangle: Quadrilateral with four right angles Theorems and Corollaries: Thm. 24: The sum of the angles of a quadrilateral is 360°. Corollary to Thm. 24: A quadrilateral is equiangular iff it is a rectangle.

  5. Lesson 2: Parallelograms and Point Symmetry Key Terms: Parallelogram: Quadrilateral with both pairs of opposite sides parallel Point Symmetry: Two points are symmetric with respect to a point iff the point is the midpoint of the line segment joining them

  6. Lesson 2: Parallelograms and Point Symmetry Theorems: Thm. 25: The opposite sides and angles of a parallelogram are equal. Thm. 26: The diagonals of a parallelogram bisect each other.

  7. Lesson 3: More on Parallelograms Theorems and Corollaries: Thm. 27: A quadrilateral is a parallelogram if its opposite sides are equal. Thm. 28: A quadrilateral is a parallelogram if its opposite angles are equal. Thm. 29: A quadrilateral is a parallelogram if two opposite sides are both parallel and equal. Thm. 30: A quadrilateral is a parallelogram if its diagonals bisect each other.

  8. Lesson 4: Rectangles, Rhombuses, and Squares Key Terms: Square: Quadrilateral with all sides equal and all angles equal . Rhombus: Quadrilateral with all sides equal

  9. Lesson 4: Rectangles, Rhombuses, and Squares Theorems: Thm. 31: All rectangles are parallelograms. Thm. 32: All rhombuses are parallelograms. Thm. 33: The diagonals of a rectangle are equal. Thm. 34: The diagonals of a rhombus are perpendicular.

  10. Lesson 5: Trapezoids Key Terms: Trapezoid: Quadrilateral that has exactly one pair of parallel sides Isosceles Trapezoid: trapezoid whose legs (non-parallel sides) are equal

  11. Lesson 5: Trapezoids Theorems: Thm. 35: The base angles of an isosceles trapezoid are equal. Thm. 36: The diagonals of an isosceles trapezoid are equal.

  12. Lesson 6: The Midsegment Theorem Key Terms: A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

  13. Lesson 6: The Midsegment Theorem Theorems: The Midsegment Theorem (Thm. 37): A midsegment of a triangle is parallel to the third side and half as long. Proof on pp 287 of textbook.

  14. Lesson 6 Practice Problem Find the measurement of BD. • BD = ½AE (midsegment thm) • BD = ½(17) (substitution) • BD = 8.5 (simplify)

  15. Lesson 6 Practice Problem 2 Find the measurement of <CBD 1. || (midsegment thm) 2. m<CBD = m<BDF (Alt. Int. <’s thm) 3. m<CBD = 26° (substitution)

  16. Chapter 7 Lab In this lab, we had to complete 3 activities each involving quadrilaterals and their parts. Activity 1: We had to compare what was true about the quadrilaterals we had talked about using a combination of Euler diagrams and Venn diagrams. Activity 2: We read about kites from a note sheet and had to list similarities that kites had with some of the other quadrilaterals we talked about in the chapter.

  17. Chapter 7 Lab (continued) Activity 3: We had to answer questions based on the equation S = (n-2)180 where S was the sum of the interior angles of a polygon with n sides, as well as the definition: a regular polygon is a convex polygon that is both equilateral and equiangular.

  18. Chapter 7 Summary In this chapter, we learned about different quadrilaterals like rectangles, parallelograms, rhombuses, and trapezoids and learned how they relate to one another. We also learned how to classify quadrilaterals by their sides, angles, and diagonals as well as revisit how to classify polygons as concave and convex. Lastly, we learned about the midsegment theorem, how it applies to all triangles and how it can be used to solve problems involving angle measures and side length.

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