Theorems
Angles
Formulas
Vocabulary
Axioms and Common Notions
100
If two angles are supplementary to congruent angles (or to the same angle), then they are congruent.
Theorem 1-2 Congruent Supplements Theorem
100
90° angle, created at the intersection of two perpendicular straight lines
Right angle
100
Midpoint formula
100
a location and has no size
A point
100
Can draw a straight line using a straight edge
Axiom #1
200
If a transversal intersects two parallel lines, then corresponding angles are congruent.
Theorem 2-2 Corresponding Angles Theorem
200
Two angles that, when added together, form 180°
Supplementary angles
200
(x,y) > (y, -x)
Rotation of 90° clockwise
200
bisects all sides at 90°
Circumcenter
200
Things that are congruent are equal to one another
Common Notion #4
300
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Theorem 4-1 Isosceles Triangle Theorem and the Converse
300
Two angles that, when added together, form 90°
Complementary angles
300
(x, y) > (-x, -y)
Rotation of 180° clockwise and counterclockwise
300
equal, but may be off by a decimal
Congruent
300
All right angles are congruent
Axiom #4
400
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Theorem 4-8 Hypotenuse Leg Theorem
400
If a transversal intersects two parallel lines, then ________ are congruent.
Corresponding angles
400
(x, y) > (-y, x)
Rotation of 270° clockwise
400
formed by two rays with the same endpoint
angle
400
If A = B and B = C, then A = C (Transitive Property)
Common notion #1
500
If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
Theorem 5-4 Angle Bisector Theorem
500
Each of the pairs of opposite angles made by two intersecting lines.
Vertical angles
500
a2 + b2 = c2
Pythagorean Theorem
500
bisecting angles
Incenter
500
The whole is greater than its part
Common notion #5