Geometry
Chapter 8: Quadrilaterals
Day
Topic
Name____________________________________
Period__________________________________
Assignment
Score
1
8.1 Find angle measures in polygons.
What are consecutive vertices? They are vertices that are endpoints of the same side.
What is a diagonal? It is a segment that joins two non-consecutive vertices.
Polygon interior angles theorem: The sum of the measures of the interior angles of a convex n-gon is (𝑛 − 2)180°.
Polygon exterior angles theorem: The sum of the measures of the exterior angles of a convex polygon, one angel at each
vertex, is 360°.
8.1 Workbook.
1-37 all
Mixed Review
p.513 39-47
/4
2
8.2 Properties of a parallelogram.
Parallelogram: It is a quadrilateral with both pairs of opposite sides parallel and congruent as well as opposite angles
are congruent.
̅̅̅̅ ≅ 𝑅𝑆
̅̅̅̅ 𝑎𝑛𝑑 𝑄𝑅
̅̅̅̅ ≅ 𝑃𝑆
̅̅̅̅.
If PQRS is a parallelogram, then 𝑃𝑄
̅̅̅̅ ∥ 𝑅𝑆
̅̅̅̅ and 𝑄𝑅
̅̅̅̅ ∥ 𝑃𝑆
̅̅̅̅.
If PQRS is a parallelogram, then 𝑃𝑄
If PQRS is a parallelogram, then ∠𝑃 ≅ 𝑅 𝑎𝑛𝑑 ∠𝑄 ≅ ∠𝑆.
If PQRS is a parallelogram, then its consecutive angles are supplementary, that is, they add up to 180°.
If PQRS is a parallelogram, then its diagonals bisect each other.
8.2 Workbook.
1-30 all
Mixed Review
p.521 46-57
/4
3
8.3 Show that a quadrilateral is a parallelogram.
What is the converse of the parallelogram stated in 8.2?
̅̅̅̅ ≅ 𝑅𝑆
̅̅̅̅ 𝑎𝑛𝑑 𝑄𝑅
̅̅̅̅ ≅ 𝑃𝑆
̅̅̅̅, then PQRS is a parallelogram.
If 𝑃𝑄
̅̅̅̅
̅̅̅̅
̅̅̅̅
̅̅̅̅
If 𝑃𝑄 ∥ 𝑅𝑆 and 𝑄𝑅 ∥ 𝑃𝑆, then PQRS is a parallelogram.
If ∠𝑃 ≅ 𝑅 𝑎𝑛𝑑 ∠𝑄 ≅ ∠𝑆, then PQRS is a parallelogram.
̅̅̅̅ and ̅̅̅̅
̅̅̅̅, then PQRS is a parallelogram.
If ̅̅̅̅
𝑃𝑄 ∥ 𝑅𝑆
𝑃𝑄 ≅ 𝑅𝑆
If consecutive angles are supplementary, that is, they add up to 180°, then PQRS is a parallelogram.
If diagonals bisect each other, then PQRS is a parallelogram.
8.3 Workbook.
1-17 all
Mixed Review
p.529 43-47
/4
4
8.4 Properties of rhombus, rectangle, and square.
There are three special types of parallelograms: rhombus, rectangle, and square.
Rhombus: it is a parallelogram with four congruent sides.
A quadrilateral is a rhombus if and only if it has four congruent sides.
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
Rectangle: it is a parallelogram with four right angles.
A quadrilateral is a rectangle if and only if it has four congruent angles.
A parallelogram is a rectangle if and only if its diagonals are congruent.
8.4 Workbook.
1-27 all
Mixed Review
p.540 65-70
/4
Square: it is a parallelogram with four congruent sides and four right angles.
A quadrilateral is a rectangle if and only if it is a rhombus and a rectangle.
5
8.5 Properties of trapezoid and kites.
Trapezoid: it is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases and the
nonparallel sides are called legs. The parallel sides include two pairs (4 angles) called base angles.
Isosceles trapezoid:
If the legs of a trapezoid are congruent, then it is an isosceles trapezoid.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
If a trapezoid is isosceles, then each pair of base angles is congruent.
A trapezoid is isosceles if and only if its diagonals are congruent.
Midsegment theorem for trapezoid: The midsegment (AKA median) connects the midpoints of the legs and is parallel
to each base. Its length is one half the sum of the lengths of the bases.
Kite: it is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
If a quadrilateral is a kite, then its diagonals are perpendicular.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
8.5 Workbook.
1-18 all
Mixed Review
p.549 44-48
/4
6
8.6 Identify special quadrilaterals.
Property
1
All sides are ≅.
2
Both pairs of opp. sides are ≅.
3
Both pairs of opp. sides are ∥.
4
Exactly 1 pair of opp. sides are ∥.
5
All angles are ≅.
6
Exactly 1 pair of opp. angles are ≅.
7
Diagonals are ⊥.
8
Diagonals are ≅.
9
Diagonals bisect each other.
Chapter 8 review.
Chapter 8 practice test.
8.6 Workbook .
1-20 all
Mixed Review
p.557 43-50
/4
7
Parallelogram
Rectangle
8
Chapter 8 Exam. You have one shot at it so give it your very best effort.
I still have questions about:
Rhombus
Square
Kite
Trapezoid
pp. 560-563 pp. 282-285
/4
1-28 all
1-29 all
p. 564 1-18 all
Total Total points /28
/36