Chapter 7 Proofs and Conditional Probability Students will be able to prove properties of quadrilaterals and using these new properties prove what the shape is. Students will develope an understanding of conditional probability and a better definition of independent probability.

Section 7.1 Students will review proofs of triangles and apply these ideas to proving properties of quadrilaterals. Students will use a 2-column proof to determine what type of shape is given. Students will learn and apply information about midsegments in triangles and trapezoids.

Quadratic Summary List of definitions and properties of the 6 main quadrilaterals. We discussed these properties and ideas of the last 2 weeks.

Trapezoid Regular Def: 1 pair of parallel sides Property: Angles on the same leg are supplementary Right Trapezoid Def: 1 pair of parallel sides and 2 right angles on the same leg Isosceles Trapezoid: Def: 1 pair of parallel sides and legs are congruent Property: Angles on the same base are congruent and diagonals are congruent Kite Def: 2 pairs of congruent consecutive sides Properties: Angles formed by non congruent sides are congruent Diagonal connecting non congruent angles bisects the other diagonal Diagonal connecting non congruent angles bisects both angles Diagonals are perpendicular

Parallelogram Def: 2 pairs of parallel sides Properties: opposite sides congruent Opposite angles are congruent Consecutive angles supplementary Diagonals bisect each other Rectangle Def: 2 pairs of parallel sides and 4 congruent angles or 4 right angles Properties: Same as a parallelogram Diagonals are congruent

Rhombus Def: 2 pairs of parallel sides and all sides congruent Properties: same as a parallelogram Diagonals are perpendicular Square Def: 2 pairs of parallel sides, 4 congruent angles or right angles and 4 congruent sides Properties: Same as a parallelogram Diagonals perpendicular, angle bisectors, bisect each other and congruent

Midsegment What is it? Connects 2 midpoints of the sides (legs) How many does a triangle have? 3 How many does a trapezoid have? 1

Midsegment in a Triangle What is special about midsegments in Triangles? Midsegment bisects sides (midpoint) Midsegment parallel to side it doesn’t touch Corresponding angles Midsegment half the length of the side it doesn’t touch

Example

Trapezoid Midsegment Trapezoid is part of a triangle Midsegment is parallel to both bases Midsegment bisects both legs Midsegment is average of both bases (b1+b2)/2

Example

Other terms and ideas Perpendicular Bisector Perpendicular to a side and bisects the side Equidistant Same distance Any point that is on the perpendicular bisector is equidistant to the endpoints of the segment being bisected These form isosceles triangles Remember altitude and height

Isosceles Triangles Proving the perpendicular bisector

Homework Worksheet on properties of quadrilaterals Worksheet on midsegments Worksheet on proofs