Studied by 1 personcpcfc
corresponding parts of congruent figures are congruent
cpctc
corresponding parts of congruent triangles are congruent
linear pair
Two adjacent angles that form a straight line (180 degrees)
vertical angle
opposite angles formed by the intersection of two lines
vertical angle theorem
Vertical angles are congruent
corresponding angles
lie on the same side of the transversal and in corresponding positions
same-side interior angles
interior angles that lie on the same side of the transversal
alternate interior angles
Interior angles that lie on opposite sides of the transversal
alternate exterior angles
two exterior angles on opposite sides of a transversal
same-side exterior angles
two exterior angles on the same side of the transversal
Same-Side Interior Angles Theorem
if 2 parallel lines are cut by a transversal, pairs of same-side interior angles are supplementary
alternate-interior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Corresponding Angles Theorem
If a transversal intersects two parallel lines, then corresponding angles are congruent.
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
ASA Theorem
If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
SAS Theorem
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.
regular polygon
all sides are congruent and all angles are congruent
SSS Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
HL Theorem (hypotenuse-leg)
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 Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
Polygon Angle Sum Theorem
The sum of the interior angle measures of a convex polygon with n sides is (n-2)180
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.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Equilateral Triangle Theorem
If a triangle is equilateral, then it is equiangular
Converse of the Equilateral Triangle Theorem
If a triangle is equiangular, then it is equilateral.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
circumscribed
circle that has all vertices of a polygon
circumcircle
a circle (idk)
circumcenter
center of circle
concurrent
3+ lines when they intersect at the same point
circumcenter theorem
the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle
Where is the circumcenter in an acute triangle?
inside
Where is the circumcenter in an right triangle?
on hypotenuse
Where is the circumcenter in an obtuse triangle?
outside
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
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
inscribed
each side of the polygon is tangent to the circle
incenter
the point of concurrency of the angle bisectors
Incenter Theorem
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
median
a segment from a vertex to the midpoint of the opposite side
centroid
The point of concurrency of the medians of a triangle
centroid theorem
The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side
altitude
a perpendicular segment from a vertex to the line containing the opposite side
orthocenter
The point of concurrency of the altitudes of a triangle
Note
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