chapter 5 review. + definition a parallelogram is a quadrilateral with both pairs of opposite sides...
TRANSCRIPT
Chapter 5 Review
+Definition
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A B
D C
ABCDNOTATION
+Sides - Paralleogram
Opposite sides are congruent
Opposite sides are parallel
+TheoremOpposite angles of a parallelogram are congruent
Consecutive angles are supplementaryA B
D C
103
10377
77
+Theorem
Diagonals of a parallelogram bisect each other.
A B
D C
+DefinitionA rectangle is a quadrilateral with four right angles.
+Rectangle
Opposite sides are congruent
Opposite sides are parallel
Sides
AnglesFour right angles
+Recall that a rectangle is a parallelogram.
Therefore a rectangle has all the same properties that a Parallelogram has! A rectangle also has some unique properties.
A Rectangle:The diagonals bisect each other
The diagonals are congruentUnique Properties
+
The diagonals of a rectangle are congruent.
CT
ER
RC = ET
Rectangle Properties
+Definition - RhombusA quadrilateral with four congruent sides.
+Rhombus
All sides are congruent
Sides
AnglesOpposite angles are congruent
Consecutive angles are supplementary
+
A Rhombus:The diagonals bisect each other
The diagonals are perpendicular
Unique Properties
Each diagonal of a rhombus bisects two angles of the rhombus
Recall that a rhombus is a parallelogram.
Therefore a rhombus has all the same properties that a Parallelogram has! A rhombus also has some unique properties.
+Definition - SquareA quadrilateral with four right angles and four congruent sides.
+Square
All sides are congruent
Sides
AnglesAll are right angles
+A Square can also be defined as a………..
A Square: The diagonals bisect each other
The diagonals are congruent
Parallelogram Rectangle Rhombus
The diagonals are perpendicular
Each diagonal of a square bisects two angles of the square
+Definition
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases
The other sides are called the legs
+Definition
An isosceles trapezoid is a trapezoid with congruent legs.
THEOREM: Base angles of an isosceles trapezoid are congruent
BASE
BASE
If trapezoid ABCD has AB = DC, then<A = <D and <B = <C
A
B
D
C
+TheoremIf both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
A B
D C
10
10
7 7
+TheoremIf both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram
A B
D C
+TheoremIf one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
A B
D C
10
10
+TheoremIf both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogramA B
D C
103
10377
77
+TheoremIf the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A B
D C
+THEOREM
The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
A
CB
X
If ABC has right <ABC and X is the midpoint of AC, then
BX = AX = XC
5
55
+THEOREM
The median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.
6 cm
10 cm
Median = (6+10)/2
Median = 16/2
Median = 8 cm8 cm
+THEOREM
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
+THEOREM
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.
+TheoremThe segment that joins the midpoints of two sides of a triangle is half as long as the third side.N
A C
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