Apexvs Geometry Semester 1

If not B, then not A (~B -> ~A)

If B, then A (B->A)

If not A, then not B (~A-> ~B)

a statement that has been proven

a statement that makes sense based on a theorem

a statement that is accepted as true without proof

A statement that is not officially defined but that is understood to be common sense.

A point at either end of a line segment or arc, or a point at one end of a ray.

a point that divides a segment into 2 congruent segments (AB+ BC=AC)

A postulate stating that if AC+ BC= AB then point C is between points A and B so AC+ CB= AB

endpoint of an angle

A ray/angle that measures 0 degrees

an angle that measures exactly 180 degrees

an angle that measures 90 degrees

an angle that measures less than 90 degrees

An angle that measures more than 90 degrees but less than 180 degrees

a ray that divides an angle into two congruent angles

Two angles that share a side and vertex

two angles whose measures have a sum of 180 degrees

a pair of supplementary angles that are adjacent

two angles whose measures have a sum of 90 degrees

Having the same size and shape. ≅

if point C lies in the interior of angle AVB then the measure of angle CVB is the measure of angle AVB

2 angles formed by a transversal that intersects two parallel lines. The angles are on opposite sides of the transversal and inside the parallel lines

The angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.

The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.

2 angles formed by a transversal that intersects two parallel lines. The angles are on the same side of the transversal and are inside the parallel lines.

2 nonadjacent angles formed on the same side of a transversal that intersects two parallel lines, with one angle interior and one angle exterior to the lines.

A law stating that the angle of incidence is congruent to the angle of reflection.

Lines that are not in the same plane. Skew lines do not intersect, and they are not parallel.

A line, ray, or segment that intersects two or more coplanar lines, rays, or segments at different points.

If a transversal intersects 2 parallel lines, then corresponding angles are congruent

if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

a transformation applied to a figure that doesn't change its shape or size at any time

scaling, rotation, and reflecting (flipping) objects to change their appearance.

shifting a set of points horizontally, vertically, or in both directions

circular movement around a single fixed point

produces a mirror image

changing the size of a figure by a scale factor. they are not rigid motions

A line that divides a figure into two congruent halves that are mirror images of each other.

A triangle with 3 acute angles

A triangle with 3 congruent sides and 3 congruent angles. they are also isosceles triangles

a triangle with at least 2 congruent sides.

a triangle with one obtuse angle

A triangle that has a 90 degree angle.

a triangle with no congruent sides

the sum of the lengths of any two sides of a triangle is greater than the length of the third side

angles on the inside of parallel lines cut by a transversal

angles on the outside of parallel lines cut by a transversal

the angles of a triangle that are not adjacent to a given exterior angle

The sum of the measures of the angles of a triangle is 180.

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

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

the measure of an exterior angle of a triangle is greater than the measures of the remote interior angles

changes the position of the figure without changing its size or shape

triangles that have their corresponding parts congruent

Congruent Parts of Congruent Triangles are Congruent

A quantity is congruent (equal) to itself. a = a

If a=b and b=c, then a=c. ( If A is congruent to B, and B is congruent to C, then A is congruent to C.)

If a = b, then b = a. (If A is congruent to B, then B is congruent to A.)

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

If two angles and the included side of one triangle are congruent to the corresponding parts of a another triangle, they are congruent

If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

A statement that proves triangles are congruent without requiring that the measures of all six pairs of corresponding parts be known.

equal ratios

A comparison of 2 quantities by division. (a,b) or (a/b)

the ratio of the lengths of two corresponding sides of two similar polygons

Figures that have the same shape but not necessarily the same size. ~

Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

the longest side of a triangle is always opposite the angle with the largest measure

the shortest side of a triangle is always opposite the angle with the smallest measure

a perpendicular segment from a vertex to the line containing the opposite side

the point where the three medians of a triangle meet

a segment from a vertex to the midpoint of the opposite side

The point where the altitudes of a triangle meet

If a line dividing a triangle is both its altitude and its median, the triangle is an isosceles triangle

The center of the only circle that can be circumscribed about a given triangle.

The center of the circle inscribed in a triangle

a segment connecting the midpoints of two sides of a triangle

a segment, ray, line, or plane that bisects a line segment at a right angle

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long.

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

if a line divides 2 sides of a triangle proportionally, then it is parallel to the third side

The product of the extremes of a proportion is equal to the product of the means

curved outward

curved inward

10 sided polygon

12 sided polygon

7 sided polygon

9 sided polygon

formula for finding the sum of measures of interior angles of polygons with n sides

the sum of the exterior angles of a convex, regular polygon

formula for finding the number of sides a regular, convex polygon

angles that share a side

a quadrilateral whose opposite sides are both parallel and equal in length

opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, any pair of consecutive angles are supplementary

a quadrilateral with four right angles (all angles are congruent) are parallelograms diagonals are congruent

near, next to, adjoining

a quadrilateral with four right angles and four congruent sides have all properties of parallelograms, rectangles, and rhombi

all sides are congruent, diagonals are perpendicular, diagonals bisect opposite angles

A quadrilateral with exactly one pair of parallel sides

a trapezoid with congruent legs and congruent base angles

the line segment joining the midpoints of the legs of a trapezoid parallel to the base

the bases are parallel, legs are non parallel, base angles are formed by the base and legs median is parallel to the bases and the length is equal to half the sum of the bases

legs are congruent, both pairs of base angles are congruent, diagonals are congruent

A pair of opposite congruent angles formed by intersecting lines

If two angles are vertical, then they are congruent

Having no length, width, or height. A point

Having length but no width or height.

having height and width

having height, width, and depth

points that lie on the same plane

points that lie on the same line

formula for finding one interior angle of a regular convex polygon