GEOMETRY 9 NOTES Date: Notes: Quadrilaterals...Trapezoids Parallelograms Non -Parallelograms...
Transcript of GEOMETRY 9 NOTES Date: Notes: Quadrilaterals...Trapezoids Parallelograms Non -Parallelograms...
Notes: Quadrilaterals
Properties of Quadrilaterals
four sides
angles add to 360°
Properties of Parallelograms
same as Quadrilaterals
opposite sides and congruent and parallel
opposite angles are congruent
diagonals bisect each other
consecutive angles are supplementary
Properties of Rectangles
same as Parallelograms
four 90° angles
diagonals are congruent
GEOMETRY 9
NOTES Date: _______________
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Isosceles
Trapezoids
Parallelograms Non-Parallelograms
Rectangles Kites
Always
Sometimes
Never Squares
Rhombi
Quadrilaterals
Trapezoids
Properties of Rhombi
same as Parallelograms
diagonals are perpendicular to each other
all sides are congruent
Properties of Squares
same as Rectangles and Rhombi
We may use properties of quadrilateral to write algebraic equations and solve for
missing variables.
Examples: Solve for the missing variables in each of the following parallelograms.
(14𝑥 + 18)°
(10𝑥 − 30)°
𝑦°
𝑧°
56 feet
42 feet 𝑥 feet
Learning Check: Solve for the missing variables in each of the following
parallelograms.
𝐴𝐶̅̅ ̅̅ = 18
𝐵𝐷̅̅ ̅̅ = 24
Perimeter = _________
288 cm
(𝑥 − 124) cm
D C
A B
4𝑥 − 37
2𝑥 + 1
2𝑥 + 100
7𝑥 + 10
14
Perimeter = _________
𝐴𝐶̅̅ ̅̅ = 45
𝐵𝐷̅̅ ̅̅ = 60
Perimeter = _________
D C
A B
NON-PARALLELOGRAMS
Properties of Trapezoids
one pair of opposite sides are parallel
- two parallel sides are called bases
- the nonparallel sides are called legs
Properties of Isosceles Trapezoids
has one pair of congruent sides
congruent diagonals
base angles are congruent
Properties of Kites
two distinct pairs of adjacent congruent sides
Examples: Use the properties of non-parallelograms to write equations and solve
for the missing variables.
Learning Check: Use the properties of non-parallelograms to write equations and
solve for the missing variables.
45°
(2𝑥 + 15)°
8𝑥 + 100
75° 3𝑦° 90°
2𝑥°
15𝑥 − 40
A B
C D
100°
x°