Geometry Quarterly #2

2 angles that add up to 90 degrees, don’t have to be adjacent

2 angles that add up to 180 degrees, don’t have to be adjacent

adjacent supplementary angles

when 2 lines intersect, the non-adjacent angles are vertical angles

all vertical angles are congruent

a line that intersects two coplanar lines at two different points

lie on the same side of the transversal and same sides of the intersecting lines

lie on the same side of the transversal and between the intersected lines

lie on opposite sides of the transversal and outside the intersected lines

are nonadjacent angles that lie on opposite sides of the transversal between the intersected lines

lie in the same plane and never intersect →- indicates parallel lines same direction. ll symbolizes parallel too.

if two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary

if two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure

if two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure

congruent

if a=b and b=c then a=c

an equal value subtracted or removed from two equal items will result in a new equal amount

if a=b then a-c=b-c

if a=b then b can replace a in any case

if two lines are cut by a transversal so that pair of same-side interior angles are supplementary, then the lines are parallel

if two lines are cut by a transversal so that any pair of alternate interior angles are congruent, they are parallel

if two lines are cut by a transversal so that any pair of corresponding angles are congruent, then the lines are parallel

through a point “P” not on the “L” there is exactly one line parallel to “L”

if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of a segment

opposite reciprocal

If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment

d=√(x₂-x₁)² + (y₂-y₁)²

y - y₁ = m ( x - x₁ )

(x₁ + x₂ / 2) , (y₁ + y₂ / 2)

rise/ run y₂-y₁ / x₂-x₁

y = mx + b

same slope

corresponding parts of congruent figures are congruent

corresponding parts of triangles are congruent (biconditional)

p if and only if q - statement can be written in that form

Two triangles are congruent if and only if corresponding pairs of angles are congruent

“if p then q” “if not q, then not p”

contrapositive of true statement is true

ex. if corresponding pairs of sides or corresponding pairs of angles are not congruent, then the triangles are not congruent

angle, included side, angle

if two angles and the included side of one triangle are congruent to. two angles and the included side of another triangle, then the triangles are congruent

a=a

of a line segment is the point that divides the segment into two segments that have the same length

all right angles are congruent; 90 degrees

goes through an angle (angle bisector), segment (segment bisector), line to form two equal parts, angles, etc

if two angles are supplements of the same angle (or congruent angles) then the two angles are congruent

if two angles are complements of the same angle (or congruent angles), then the two angles are congruent

all angle measures are the same, all side lengths are the same (equiangular and equilateral)

side, included angle, side

if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the the triangles are congruent

perpendicular bisector of a line segment is a line perpendicular to the segment at the segments midpoint. Form right angles

side, side, side

if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent

AAA & SSA

angle, angle, side

if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.

hypotenuse, leg

if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent

a² + b² = c² (a bottom, b side, c hypotenuse)

the sum of the angle measures of a triangle is 180 degrees

the sum of the measures of the interior angles of a convex polygon with “n” sides is n-2(180)

in, dip in shape “M”

out, up ;“O”;”G"

an angle formed by one side of a polygon and the extension of an adjacent side. Exterior angles form linear pairs with the interior angles

an interior angle that is not adjacent to the exterior angle

the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles

a triangle with at least two congruent sides

if two sides of a triangle are congruent, then the two angles opposite the sides are congruent

if two angles of a triangle are congruent, then the two sides opposite the angles are congruent

a triangle with 3 congruent sides

a triangle with 3 congruent angles

if a triangle is equilateral, then it is equiangular

if a triangle is equiangular, then it is equilateral

the sum of any two side lengths of a triangle is greater than the third-side length **tip - add two smallest sides**

circle is called circumcircle

the center of the circle is called the circumcenter

Three or more lines are concurrent if they intersect at the same point. The point of intersection is called the point of concurrency.

the perpendicular bisectors of the sides of a triangle intersect at a point that is equidistant from the vertices of the triangle PA=PB=PC

circumcenter is inside the triangle

circumcenter is on the triangle

circumcenter is outside the triangle

length of the perpendicular segment from the point to the line

if a point is on the bisector of an angle, then it is equidistant from the sides of the angle <APC≅<BPC so… AC = BC

if a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

AC = BC so… <APC≅<BPC

if each side of the polygon is tangent (on) to the circle. The inscribed circle is called the incircle

The incenter of the triangle

the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle

of a triangle is a segment whose endpoints are a vertex of a triangle and the midpoint

the intersection (point of concurrency) of the three medians of a triangle

inside the triangle; center of gravity of a triangle

the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side

perpendicular segment from a vertex to the line containing the opposite side; every triangle has 3 altitudes; not a bisector, doesn’t necessarily go to midpoint

can be inside, outside, or on the triangle

the intersection (or point of concurrency) of the lines that contain the altitudes; can be inside, outside, or on the triangle

inside triangle

on triangle

outside triangle

perpendicular bisectors

angle bisectors

medians

altitudes