4.5 Proving Quadrilateral Properties
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Transcript of 4.5 Proving Quadrilateral Properties
Objective:Prove quadrilateral conjectures by using triangle congruence postulates and theorems
4.5 Properties of Quadrilaterals
Warm-Up:How are the quadrilaterals in each pair alike? How are they different?
Parallelogram vs Square
Rhombus vs Square
Alike:
Different:
Alike:
Different:
Opp sides || & 4 = sidesOpp <‘s = Diagonals perp.
Sq has 4 right <‘s
Sq 4 right <‘sSq 4 sides
Quadrilateral: Any four sided polygon.
Trapezoid:A quadrilateral with one and only one pair of parallel sides.
Parallelogram:A quadrilateral with two pairs of parallel sides.Rhombu
s: A quadrilateral with four congruent sides.
Rectangle:A quadrilateral with four right angles.Square
: A quadrilateral with four congruent sides and four right angles.
PROPERTIES OF SPECIAL QUADRILATERALS:
PARALLELOGRAMS:Both pairs of opposite sides are parallelBoth pairs of opposite sides are congruentBoth pairs of opposite sides angles are congruentConsecutive angles are supplementary
Diagonals bisect each other
A diagonal creates two congruent triangles (it’s a turn – NOT a flip)
M
LP
G
Theorem: A diagonal of a parallelogram divides the parallelogram into two congruent triangles.
PROPERTIES OF SPECIAL QUADRILATERALS:
RECTANGLES:Rectangles have all of the properties of parallelograms plus:
Four right angles
Congruent Diagonals
Perpendicular Sides
PROPERTIES OF SPECIAL QUADRILATERALS:
RHOMBUSES:Rhombuses have all of the properties of parallelograms plus:
Four congruent sides
Perpendicular diagonals
Diagonals bisect each other
PROPERTIES OF SPECIAL QUADRILATERALS:
SQUARES:Squares have all of the properties of parallelograms, rectangles & rhombuses.
Example:
Find the indicated measures for the parallelogram WXYZ
m<WXZ = _____
m<W = _____
m<ZXY = _____
XY = _____
m<WZX = _____Perimeter of WXYZ= _____
W X
Z Y
2.2
5
𝟐𝟓𝟎 𝟏𝟐𝟎𝟎
Example: ABDE is a parallelogram & BC BD
If m<BDC = , find m<EAB. _______
A B
DE C
If m<DBC = , m<BCD=6x, find m<EAB ______
If m<DBC = , m<BCD=6x, find m<ABD ______
Objective:Identify the missing component of a given parallelogram through the use of factoring.
Parallelograms & Factoring
Warm-Up:
What is the first number that has the letter “a” in its name?
Given: Prove:
Parallelogram ABCD with diagonal BDAB CD & AD CB
STATEMENTS REASONS
Theorem: Opposite sides of a parallelogram are congruent.