1/62
Looks like no tags are added yet.
Name | Mastery | Learn | Test | Matching | Spaced |
---|
No study sessions yet.
Adjacent Angles
Angles that share a vertex and a common side. They cannot share interior angles.
Midpoint
A point that divides a segment into two congruent segments.
Congruent
Same size, same shape.
Congruent Segments
Segments with the same lengths.
Congruent Angles
Angles with the same measure.
Collinear
Points that are present on the same line.
Non-Collinear
Points that are not present on the same line.
Coplanar
Points that are on the same plane.
Non-Coplanar
Points that do not lie on the same plane.
Between
A point between two distinct points.
Segment
A part of a line with two endpoints, that includes all points in between.
Linear Pair
Two adjacent angles that do not share a common vertex or side. These form a line.
Angle Bisector
A ray in the interior of the angle that forms two congruent angles.
Postulate
A statement accepted as true without proof.
Theorem
A proven statement.
Line Postulate
Through any two points, there is exactly one line.
Parallel Postulate
Through a point not on a line, there is exactly one line parallel to the given line.
Perpendicular Postulate
Through a point not on a line, there is exactly one line perpendicular to the given line.
Linear-Pair Postulate
If two linear pairs create a line, they are supplementary. (You need to establish that the angles form a linear pair.)
Segment Addition Postulate
If point B is collinear with and between points A and C, then AB + BC = AC. (You must identify points A, B, and C, confirming their collinearity.)
Angle Addition Postulate
If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. (You need to confirm that point D lies in the interior.)
Reflexive Property
Equality a = a.
Congruency
Line AB is congruent to line AB.
Symmetric Property
Equality if a = b, then b = a.
Transitive Property
Equality if a = b, and b = c, then a = c.
Substitution Property
If a = b, then b can be replaced by a and vice versa.
Distributive Property
a(b + c) = ab + ac.
Addition Property
Equality if a = b, then a + c = b + c.
Subtraction Property
Equality if a = b, then a - c = b - c.
Multiplication Property
Equality if a = b, then ac = bc.
Division Property
Equality if a = b, then a/c = b/c.
Median
A segment drawn from a vertex to the opposite side.
Midsegments
Segments that connect the midpoints of two sides of a triangle.
Midsegment Theorem
The length of a midsegment is always half of the base of the triangle. It is also parallel to the base of the triangle. (You must identify the triangle and the midsegment.)
Parallelogram
A quadrilateral with two pairs of parallel sides.
Rectangle
An equiangular parallelogram. All the angles measure 90 degrees.
Diagonals
Segments that connect opposite vertices in a parallelogram.
Corresponding Angles
Angles that are in the same position on two parallel lines cut by a transversal.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. (You need to establish that the lines are parallel.)
Converse of Corresponding Angles Postulate
If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. (You need to declare that they are cut by a transversal and that angles are congruent.)
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. (You need to confirm the angle measurements.)
Linear Pair Postulate
If two angles form a linear pair, they are supplementary. (You must declare the angles are adjacent.)
Alternate Interior Angle Theorem
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. (You need to establish that the lines are parallel.)
Alternate Exterior Angle Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. (You need to establish that the lines are parallel.)
Same-Side Interior Angle Theorem
If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. (You need to establish that the lines are parallel.)
Same-Side Exterior Angle Theorem
If two parallel lines are cut by a transversal, then the pairs of same-side exterior angles are supplementary. (You need to establish that the lines are parallel.)
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (You must identify the exterior angle and the relevant interior angles.)
Quadrilateral Sum Theorem
The sum of the interior angles of a quadrilateral is always 360 degrees. (You need to confirm the quadrilateral's shape.)
Triangle Sum Theorem
The sum of the interior angles of a triangle is always 180 degrees. (You need to confirm the triangle's shape.)
Right Triangle Complements Theorem
The two non-right angles in a right triangle are complementary (their measures add up to 90 degrees). (You must establish that one angle is a right angle.)
Converse to the Same Side Interior Angle Theorem
If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel. (You need to confirm the supplementary angles and declare the lines being cut by the transversal.)
Converse to the Same Side Exterior Angle Theorem
If two lines are cut by a transversal and the same-side exterior angles are supplementary, then the lines are parallel. (You need to confirm the supplementary angles and declare the lines being cut by the transversal.)
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or congruent angles), then they are congruent to each other. (You must declare the angles that are supplementary to the same angle.)
Congruent Complements Theorem
If two angles are complementary to the same angle (or congruent angles), then they are congruent to each other. (You must declare the angles that are complementary to the same angle.)
Linear Pair Theorem
If two angles form a linear pair, they equal 180 degrees. (You need to declare that they form a linear pair.)
Right Angle Theorem
All right angles are congruent (they all measure 90 degrees).
Vertical Angles Theorem
Vertical angles, formed when two lines intersect, are congruent. (You need to declare that the angles are vertical.)
if perpendicular —> congruent adjacent angles
if two lines are perpendicular, then their adjacent angles are congruent
if congruent adjacent angles, then perpendicular
if adjacent angles are congruent, then the two lines are perpendicular
congruent segments theorem (biconditional)
AB is congruent to CD if and only if AC is congruent to BD
congruent angle theorem (biconditional)
<AOC is congruent to <BOD if and only if <AOB is congruent to <COD
parallel-parallel theorem
if two lines are parallel to the same line, then they are parallel
double perpendicular theorem
in the same plane, if two lines are perpendicular to the same line, then they are parallel