Section 1
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midpoint formula
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Date created
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Cards (100)
Section 1
(56 cards)
midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
Hypotenuse Leg Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Triangle Midsegment Theorem
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.
obtuse triangle
a triangle with one obtuse angle
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Midpoint
A point that divides a segment into two congruent segments
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary
Angle-Angle-Side (AAS)
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent
Side-Side-Side (SSS)
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
complementary angles
Two angles whose sum is 90 degrees
Transitive
If a=b and b=c, then a=c
Transversal
a line that intersects two or more parallel lines
Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same-side interior angles are supplementary.
Plane
a flat surface that extends forever
equilateral triangle
A triangle with three congruent sides and angles
altitude of a triangle
The altitude of a triangle is a line segment from a vertex that is perpendicular to the opposite side
right triangle
a triangle with one right angle
acute triangle
a triangle with 3 acute angles (less than 90 degrees)
median of a triangle
a segment from a vertex to the midpoint of the opposite side
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
congruent shapes
two figures that have the same size and shape
adjacent angles
Angles that have a common side and a common vertex (corner point).
Orthocenter
The point of concurrency of the altitudes of a triangle
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
The definition of congruent triangles; if two triangles are congruent, then the corresponding parts of the congruent triangles are congruent
linear pair
A pair of adjacent angles whose noncommon sides are opposite rays.
Collinear points
Points on the same line
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Angle Addition Postulate
If P is in the interior of <RST, then m<RSP + m<PST = m<RST
corresponding angles
Angles in the same place on different lines
Ruler Postulate
The points on a line can be matched one to one with the real numbers and you can use it to find the distance between two points
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
Side-Angle-Side (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
isosceles triangle
A triangle that has 2 equal sides and 2 equal angles
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Alternate Exterior Angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
Reflexive Property
A quantity is congruent (equal) to itself. a = a
angle bisector
a ray that divides an angle into 2 congruent angles
Alternate exterior angles theorom
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
alternate interior angles
Congruent angles between the same pair of parallel lines and on opposite sides of a transversal
supplementary angles
Two angles whose sum is 180 degrees
scalene triangle
a triangle with no congruent sides or angles
Angle-Side-Angle (ASA)
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.
Converse of the Angle Bisector Theorem
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
Coplanar points
points that lie on the same plane
Substitution
<1 + <4 = 180 <4 is congruent to <7 <1 + <7 = 180
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Section 2
(44 cards)