Geometry HH Flash Cards
Slope of perpendicular Lines
Slope values will be opposite reciprocals take the one slope value, and flip it upside down. Put this together with the sign change,
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines, a pair of opposite congruent angles formed by intersecting lines.
Area of a rectangle
A= L*W
Heron's Formula
A=√(s(s-a)(s-b)(s-c))
Segment Addition Postulate
AB+BC=AC
Right Angle
An angle that measures exactly 90 degrees
Standard Form
Ax + By = C
Circumference Formula
C=pi*d OR C=2*pi*r
Pie
Circumference/Diameter
Theorem 5-1
If a segment joins the midpoints of two sides of a triangle, then that segment is parallel to the third side, and half as long as the third side
Postulate 3.1/ Corresponding angles Postulate
If a transversal intersects two parallel lines, then the corresponding angles are congruent
Therom 3-2/ Same Interior Angles Theorem
If a transversal intersects two parallel lines, then the same-side interior angles are supplementary
Therom 3-1/ Alternate Interior Angles Theorem
If a tranversal intersects two parallel lines, then same-side interior angles are supplementary
Theorem 6-17
If kite, then diagonals are perpendicular
Converse
If lines // SSI are supplementary
Contrapositive
If not q then not p
Theorem 6-6
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram
Law of Syllogism
If p ->q and q->r are ture conditional statements, then p->r is true
Conditional Statements
If p, then q p= Hypothesis q=Conclusion
Law of detachment
If p, then q p= true Conclusion= q is true
Theorem 6-11
If rectangle then, congruent diagonals
Hypotenuse Leg Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
Corresponding Parts Congruent Triangles Congruent
If you can prove that two triangles are congruent by ASA, AAS, SSS, HL, or SAS, you know that their corresponding parts must be congruent as well.
Euler's Line
In a triangle, the line on which the orthocenter, centroid, and circumcenter lie.
Angles of a triangle
Line opposite the biggest angle is the longest side
Point
Location, has no size, no dimension. Thru two points there is 1 line
Circumcenter of a right Triangle
Midpoint of hypothenuse
Quadrilateral
a four-sided polygon
Area of a circle
pi*r²
Acute Equilateral Triangle
triangle with all angles and sides congruent with angles that are less than 90 degrees
Obtuse Scalene Triangle
triangle with one angle of more than 90 degrees but less than 180 degrees and 2 acute angles;none of the angles are congruent
Complementary Angles
two angles whose sum is a right angle, Two angles whose sum is 90 degrees
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
Slope-Intercept
y=mx+b
Plane
flat surface that extends infinitely in all directions. A line is formed when two planes intersect. 3- non collinear points define a plane
Ray
has an endpoint and goes infinite in the other direction
Line Segment
has two endpoints
Converse
if // AIA congruent, if AIA congruent, //
Converse
if //, corr congruent. If corr,//
Theorem 6-9
if it is a rhombus, then each diagonal bisects two angles
Inverse
if not p, then not q
Converse
if q, then p
Isosceles Triangle Theorem
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
4 centers of an isosceles triangle
in an isoscles triangle, the 4 centers of a triangle are on the same line
Slope of parallel lines
parallel lines have the same slope — and lines with the same slope are parallel.
Diagonal angles of a rhombus
If a diagonal of a p-gram bisects 2 angles then it is a rhombus
Theorem 6-10
If a quadrilateral is a rhombus, then it's diagonals are perpendicular.
Circumcenter
Point where perpendicular bissectors meet, Perpendicular bisectors
Converse of ITT
2 angles of triangle congruent -> corresponding sides congruent
Sides of a triangle
2 smaller sides have to be greater than the longest side
Square
(geometry) a plane rectangle with four equal sides and four right angles
Midpoint Formula
(x₁+x₂)/2, (y₁+y₂)/2
Point-Slope
(y-y1)=m(x-x1)
Regular Polygon
1.) All sides congruent 2.) All angles, congruent
Indirect Proof
1.) Assume opposite of what you are trying to prove 2.) Show assumption leads to a contradiction 3.) Hence,
Polygon
1.) Closed 2.) Straight Lines 3.) No intersect
A quad is a p-gram if..
1.) Opposite sides are parallel 2.) Diagonal angles are congruent 3.) Opposite sides are congruent 4.) Diagonals bisect each other 5.) 1 pair of sides are congruent and parallel
Altitude
Height of a triangle
Biconditional Statements
Must have a true conditional and converse, PIFFQ
Supplementary Angles
Two angles whose sum is 180 degrees
AAS
Two triangles are congruent if 2 sets of corresponding angles and one set on non-included sides are congruent.
ASA
Two triangles are congruent if 2 sets of corresponding angles and their included side are congruent.
SAS
Two triangles are congruent if 2 sets of corresponding sides and their included angles are congruent.
SSS
Two triangles are congruent if all 3 sets of corresponding sides are congruent.
Orthocenter
Where altitudes meet
Rhombus
a parallelogram with four equal sides
Rectangle
a parallelogram with four right angles
Trapezoid
a quadrilateral with exactly one pair of parallel sides
Kite
a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
Parallelogram
a quadrilateral with two pairs of parallel sides
Right Isosceles Triangle
a right triangle with two congruent legs
Scalene Triangle
a triangle with no two sides of equal length, A triangle with no congruent sides.
Equilateral Triangle
a triangle with three congruent sides
Isosceles Triangle
a triangle with two equal sides
Obtuse Angle
an angle between 90 and 180 degrees
Acute Angle
an angle less than 90 degrees but more than 0 degrees
Incenter
angle bisectors
Obtuse angle if
a²+b²<c²
90 degree angle if
a²+b²=c²
Pythagorean Theorem
a²+b²=c²
Acute angle if
a²+b²>c²
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Line
infinite in both directions, straight two line segments intersect at a point
Centroid
intersection of medians
Transversal
is a line that passes through two or more other lines in the same plane at different points. When the lines are parallel, as is often the case, a transversal produces several congruent and several supplementary angles.
parallel
lines that are on the same plane, and don't intersect
Circumcenter of an obtuse triangle
located outside of the triangle
Orthocenter of an obtuse Triangle
located outside of the triangle
Slope Formula
m = (y2 - y1) / (x2 - x1)
Skew
non-coplaner lines
non- collinear
not on the same line
Semi- perimeter
one half of the perimeter, s=(a+b+c)/2
Isosceles Trapezoid
one pair of parallel sides, a trapezoid whose nonparallel opposite sides are congruent
Theorem 6-2
opposite angles of a parallelogram are congruent
Theorem 6-1
opposite sides of a parallelogram are congruent
collinear
same line 2 lines can be;
Median
segment from vertex to opposite midpoint
Adjacent Angles
share a ray, next to
Theorem 6-3
the diagonals of a parallelogram bisect each other
Orthocenter of a right Triangle
the point in which the lines containing the altitudes are concurrent