Geometry Chapter 5 Flashcards
A square is an…
equilateral and equiangular parallelogram. Thus a square is both a rectangle and a rhombus.
The diagonals of a rhombus are…
perpendicular bisectors of eachother.
Minimum Definition of a rectangle is:
A rectangle is a parallelogram having one right angle
The opposite sides of a parallelogram
are parallel/congruent
AB=CD AD=BC
Diagonal Properties of Rectangles
Diagonals bisect each other, are congruent, and form 2 pairs of congruent triangles.
The Diagonals of a parallelogram…
Bisect eachother and divides it into two congruent triangles.
A rectangle is an…
equiangular parallelogram
If a parallelogram has congruent diagonals,
then it is a rectangle.
If ABCD is a parallelogram and AC=BD, then ABCD is a rectangle.
If a line is drawn from the midpoint of one side of a triangle and parallel to a second side,
then it passes through the midpoint of the third side
if M is the midpoint of AB and MN is parallel to AC, then N is the midpoint of BC
A square has all the properties of…
both the rhombus and the rectangle.
The base angles of an isosceles trapezoid…..
are congruent
If AB=CD then angle A=Angle D
If three or more parallels cut off congruent segments on one transversal…
then they cut off congruent segments on any other transversal.
If line 1 is parallel to lines 2 and 3 and segments a and b of transversal AB are congruent, then segments c and d of transversal CD are congruent.
If a quadrilateral’s diagonals bisect each other
Then it is a parallelogranm
The medians of a triangle meet in a point…
which is two thirds of the distance from any vertex to the midpoint of the opposite side.
if AN, BP, and CM are medians to the triangle, then they meet in a point G which is two-thirds of the distance from A to N, B to P, and C to M.
What has all the properties of a parallelogram?
A rectangle, rhombus, or square has all the properties of a parallelogram.
If a parallelogram has a right angle and two congruent adjacent sides…
then it is a square
If a line joins the midpoints of two sides of a triangle,
then it is parallel to the third side and its length is one-half the length of the third side.
If M and N are the midpoints of AB and BC, then MN is perpendicular to AC and MN =1/2 AC
Principle 8: A quadrilateral is a parallelogram…
if its opposite sides are congruent
If AB=CD and AD=BC then ABCD is a parallelogram
The length of the median to the hypotenuse of a right triangle…
equals one-half the length of the hypotenuse.
If CM is the median to hypotenuse AB, then CM=1/2 AB
CM=AM=MB
Principle 7: The diagonals of a rhombus…
form four congruent triangles
Triangle I=II=III=IV
Parallelogram
A quadrilateral whose opposite sides are parallel.
True or False: The diagonals of a rhombus do not bisect the vertex angle.
False… They do.
AC bisects angle A and C
True or False: A quadrilateral is a parallelogram if its opposite sides are parallel
True
Trapezoid
A quadrilateral having two and only two, parallel sides. The bases of the trapezoid are its parallel sides; and the legs are its nonparallel sides. The median of the trapezoid is the segment joining the mipoints of its legs.
Bases: AD and BC
Legs: AB and CD
if M and N are midpoints then MN is the median
The median of a trapezoid is…
Parallel to its bases, and its length is equal to one-half of the sum of their lengths.
If MN is the median of trapezoid ABCD, then MN is Parallel to AD, and MN is parallel to BC and m=1/2(b+b’)
Diagonal Properties of Parallelograms
Diagonals bisect each other and form 2 pairs of congruent triangles.
The consecutive angles of a parallelogram…
are supplementary
angle A is the supplement of both angle B and D
Isosceles trapezoid
A trapezoid whose legs are congruent.
the base angles of a trapezoid are the angles at the ends of its longer base. Angle A and D are the base angles of isosceles trapezoid ABCD.
Diagonal Properties of Rhombuses
Diagonals bisect eachother, are perpendicular, bisect vertex angles, forms 2/4 congruent triangles.
All sides of a rhombus are…
Congruent
Each angle of a rectangle…
Is a right angle.
Diagonal Properties of Squares
Diagonals bisect eachother, are congruent, are perpendicular, bisect vertex angles, form 2/4 congruent triangles.
Minimum definition of a rhombus:
A rhombus is a parallelogram having two congruent adjacent sides.
A rhombus is an…
equilateral parallelogram.
The diagonals of a rectangle are…
Congruent
AC=BD
The opposite angles of a parallelogram…..
Are congruent
If a parallelogram has congruent adjacent sides…
then it is a rhombus.
Principle 10: A quadrilateral is a parallelogram…
If its opposite angles are congruent
If the base angles of a trapezoid are congruent…
the trapezoid is isosceles
if angle A=angle D then AB=CD
If two sides of a quadrilateral are congruent and parallel…
then the quadrilateral is a parallelogram.
