Studied by 1 personThe diagonals of a rectangle are
congruent and bisect each other
The diagonals of a rhombus are
perpendicular
diagonals of a square
congruent, bisect each other, perpendicular, bisect vertex angles
Diagonals of a parallelogram
bisect each other
Sides of a rhombus
all sides are congruent and opposite sides are parallel
sides of a kite
2 pairs of consecutive sides are congruent
angles of a kite
1 pair of opposite angles are congruent
diagonals of a kite
are perpendicular
Parallelogram
Def: a quadrilateral with 2 pairs of opposite sides parallel
Properties:
-Opposite sides congruent
-Opposite angles congruent
-Consecutive angles are supplementary
-diagonals bisect each other (same midpoint)
Rectangle
Def: a parallelogram (2 pairs of parallel sides) with 4 right angles
Properties:
-Opposite sides congruent
-4 right angles
-Consecutive angles are supplementary
-diagonals bisect each other (same midpoint)
-diagonals are congruent
rhombus (plural: rhombi)
Def: a parallelogram (2 pairs of parallel sides) with 4 congruent sides
Properties:
-All sides congruent
-Opposite angles congruent
-Consecutive angles are supplementary
-diagonals bisect each other (same midpoint)
-diagonals bisect vertex angles
-diagonals are perpendicular
Square
Def: a parallelogram (2 pairs of parallel sides) with 4 right angles AND 4 congruent sides
Properties:
-ALL sides congruent
-4 right angles
-Consecutive angles are supplementary
-diagonals bisect each other (same midpoint)
-diagonals are congruent AND perpendicular
-diagonals bisect vertex angles
Trapezoid
Def: a quadrilateral with ONE pair of parallel sides
Properties:
-Angles on a leg are supplementary
-midsegment (median) is average of the bases
Isosceles Trapezoid
Def: a quadrilateral with ONE pair of parallel sides and one pair of congruent sides
Properties:
-Angles on a leg are supplementary
-Legs are congruent
-Base angles are congruent
-Diagonals are congruent
-midsegment (median) is average of the bases
Kite
Def: a quadrilateral with NO pairs of parallel sides
Properties:
-2 pairs of consecutive congruent sides
-diagonals are perpendicular
-longer diagonal bisects the shorter diagonal (and vertex angles)
-1 pair of opposite angles congruent
sides of a square
all sides are congruent and opposite sides are parallel
Sides of a rectangle
Opposite sides are congruent and parallel
sides of a trapezoid
one pair of parallel sides
Angles in a Parallelogram
Opposite Angles are Congruent.
Consecutive Angles are Supplementary.
Angles in a square
4 right angles
Dialations
a transformation that changes the size of a figure but not its shape. It involves stretching or shrinking the original figure by a certain scale factor.
In order for two polygons to be similiar all of their corresponding angles must have corresponding ______ and must be __________
sides, proportional
Proportions are used to solve for?
Missing sides of similar figures.
A well scaled figure has corresponding angles that are _____ that are ____________
sides,proportional
When lines are dialated, they are?
paralell
The constant of proportionality is called the?
scale factor
Slope formula
New/Old
Dialation Rule?
Big/Little or Right/Leftb
Dilation steps
1.Mark the center of dilation
2.Count from the center of each vertex
3.Multiply by the Scale Factor and plot from the center of dilation
4.Determine the new coordinate from the origin.
When two figures have the same shape but not the same size they are?
similar (~)
Two figures are similar if and only if one figure can be?
Transformed
Angle-Angle Similarity(AA~)
If two angles of one triangle are congruent to two angles of another triangle, then the two are congruent.
Side-Side-Side Similarity(SSS~)
If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.
Side-Angle-Side Similarity (SAS~)
If the measure of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the two triangles are similar.
If two triangles are similar, then the measures of the corresponding _____________ are proportional to the measures of the corresponding sides (and perimeter)
Altitudes
Note
Flashcard