Quadrilaterals Postulates and Theorems
Trapezoid
1 pair
Quadrilateral
4 sides ,4 angles , sum of interior angles is 360, of exterior.
Midsegment of a Trapezoid
A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid. A trapezoid midsegment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.
A rectangle has all the characteristics of a ____________.
All angles are right angles by definition. The diagonals are congruent.
The diagonals of a rhombus _____________ each angle.
All sides have equal length. Opposite sides are parallel, and opposite angles are equal (it is a Parallelogram). The altitude is the distance at right angles to two sides. And the diagonals "p" and "q" of a rhombus bisect each other at right angles.
The diagonals of a rhombus are _____________.
All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary). All sides are congruent by definition. The diagonals bisect the angles.
The diagonals of a rectangle are ____________.
As you can hopefully see, both diagonals equal 13, and the diagonals will always be congruent because the opposite sides of a rectangle are congruent allowing any rectangle to be divided along the diagonals into two triangles that have a congruent hypotenuse.
The sides of a rhombus are __________.
Definitions and formulas for the perimeter of a rhombus, the area of a rhombus, properties of the angles and sides of a rhombus
The exterior angles of a quadrilateral equal ______.
Exterior angles of a quadriltaeral add up to 1080° , each exterior angle is equal to the interior angle subtracted from 360°. The formula for checking sums of interior a...ngles of any multilateral figure is (n-2)*180°, hence a quadilateral has 4 sides (n) (4-2)*180°=360°.
A parallelogram has all the characteristics of a __________________.
If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi. If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid.
The angles of a rectangle are _______.
The angles of a rectangle are 90+90+90+90= which make it to 360 degrees.
Base angles of an isosceles trapezoid
The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base).
Diagonals of a trapezoid are ___________.
The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are the same length (congruent). The angles on either side of the bases are the same size/measure (congruent).
A rhombus has all the characteristics of a ___________.
The diagonals bisect the angles.
Base of an Isosceles trapezoid
The properties of the trapezoid are as follows: The bases are parallel by definition. Each lower base angle is supplementary to the upper base angle on the same side. The properties of the isosceles trapezoid are as follows: The properties of trapezoid apply by definition (parallel bases).
The sum of the interior angles of a quadrilateral is ______.
The sum of the measures of the *interior* angles of a quadrilateral is always 360 degrees. To understand why this is true, recall that the sum of the interior angles of a triangle is 180 degrees. Now, in any quadrilateral, we can draw a diagonal, splitting it into two triangles.
Legs of an Isosceles trapezoid
There is a special kind of trapezoid called an isosceles trapezoid. An isosceles trapezoid is a trapezoid in which the legs are equal in length. Remember that the legs are the non-parallel sides, as opposed to the parallel bases. You'll notice that in the first trapezoid in this lesson (above), the legs are NOT equal.
The diagonals of a parallelogram _______ _______ ________.
To create a parallelogram just think of 2 different pairs of parallel lines intersecting. ABCD is a parallelogram. Click on the button below to turn the pure parallel lines into a parallelogram.
The consecutive angles of a parallelogram are ____________.
Two interior angles of a parallelogram are called the consecutive angles if some side of the parallelogram is the common side of these two angles. Figure 1 shows the parallelogram ABCD. The consecutive angles of the parallelogram ABCD are the angles. LA and LB; LB and LC; LC and LD; LA and LD.
A square has all the characteristics of a __________ and __________.
a square is a shape that has four equal sides, and four 90 degree angles. 1) All sides are congruent. 2) All angles are right angles. 3) The sum of the interior angles of a square will always be 360 degrees. 4) A square is a rectangle, while a rectangle is not a square.
Rectangle
all properties of a parallelogram, all angles are 90 (congruent ) diagonals are congruent
Rhombus
all properties of parallelogram , all sides are congruent, diagonals are perpendicular,bisect angles
Isosceles Trapezoid
all properties of quadrilateral , 1 pair of parallel
Parallelogram
all properties of quadrilateral, opposite sides are congruent,opposite angles, consecutive angles are supplementary.
Square
all properties of rhombus , all properties of rectangle
The opposite angles of a parallelogram are _____________.
here are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). Opposite angels are congruent (D = B). Consecutive angles are supplementary (A + D = 180°). If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Angles · Algebra 1 · Algebra 2 · Vectors
The opposite sides of a parallelogram are ___________ and ___________.
n Euclidean geometry, a parallelogram is a (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
