Download Chapter 10: Introducing Geometry

Chapter 10: Introducing Geometry
10.5
More About Quadrilaterals
10.5.1. Properties of Quadrilaterals
10.5.1.1. parallelogram – quadrilateral with two pairs of parallel sides
10.5.1.1.1. a quadrilateral is a parallelogram if and only if
10.5.1.1.1.1.
opposite sides are congruent
10.5.1.1.1.2.
one pair of opposite sides are both parallel and congruent
10.5.1.1.1.3.
opposite angles are congruent
10.5.1.1.1.4.
consecutive angles are supplementary
10.5.1.1.1.5.
diagonals bisect each other
10.5.1.2. rectangle – quadrilateral with four right angles
10.5.1.2.1. a parallelogram is a rectangle if and only if
10.5.1.2.1.1.
it has at least one right angle
10.5.1.2.1.2.
its diagonals are congruent
10.5.1.3. rhombus – quadrilateral with four congruent sides
10.5.1.3.1. a parallelogram is a rhombus if and only if
10.5.1.3.1.1.
it has four congruent sides
10.5.1.3.1.2.
its diagonals bisect its angles
10.5.1.3.1.3.
its diagonals are perpendicular bisectors of each other
10.5.1.4. square – quadrilateral with four right angles and four congruent sides
10.5.1.4.1. a parallelogram is a square if and only if
10.5.1.4.1.1.
it is a rectangle with four congruent sides
10.5.1.4.1.2.
it is a rhombus with a right angle
10.5.1.4.1.3.
its diagonals are congruent and perpendicular bisectors of each
other
10.5.1.4.1.4.
its diagonals are congruent and bisect the angles
10.5.1.5. trapezoid – exactly one pair of opposite sides parallel
10.5.1.6. kite – at least two pairs of adjacent sides congruent; no side used twice in the
pairs
10.5.2. Quadrilaterals and Geometric Constructions
10.5.2.1. See appendix D p. 879
10.5.2.2. What I expect you to be able to do:
10.5.2.2.1. D.1
10.5.2.2.1.1.
copy a circle,
10.5.2.2.1.2.
copy a line segment, and
10.5.2.2.1.3.
copy an angle
10.5.2.2.2. D.2
10.5.2.2.2.1.
construct a perpendicular bisector and
10.5.2.2.2.2.
bisect an angle
10.5.3. What-If Questions about Quadrilaterals
10.5.4. Problems and Exercises p. 643
10.5.4.1. Home work: 1-22, 33, 35, 37, 39, 41, 48, 51