Theorems Flashcards
Theorem 4.2
If two angles are adjacent and supplementary, then they form a linear pair
Theorem 4.1
All right angles are congruent
Theorem 4.3
Angles that form a linear pair are supplementary
Theorem 4.4
If one angle of a linear pair is a right angle, then the other angle is also a right angle
Theorem 4.5
Vertical angle theorem
Vertical angles are congruent
Theorem 4.6
Congruent supplementary angles are right angles.
Theorem 5.1
The conditional p—>q is equivalent to the disjunction~p or q
Theorem 5.2
Contrapositive rule
A conditional statement is equivalent to its contrapositive. In other words, p—>q is equivalent to ~q—>~p
Theorem 6.1 congruent segment bisector theorem
If two congruent segments are bisected, then the four resulting segments are congruent
Theorem 6.2
Segment congruence is an equivalence relation
Theorem 6.4
Complements of congruent Angles are congruent
Theorem 6.5
Angle congruence is an equivalence relation
Theorem 6.6 adjacent angle sum theorem
If two adjacent angles are congruent to another pair of adjacent angles, then the larger angles formed are congruent
Theorem 6.7 adjacent angle portion theorem.
If two angles, one in each pairs of adjacent angles, are congruent, and the larger angle formed are also congruent, then the other two angles are congruent
Theorem 6.8 congruent angle bisector theorem.
If two congruent angles are bisected, the four resulting angles are congruent
Theorem 6.9
Triangle congruence is an equivalence relation
Theorem 6.10
Circle congruence is an equivalence relation
Theorem 6.11
Polygon congruence is an equivalence relation
Theorem 6.12 alternate exterior angle theorem
Two lines intersected by a transversal are parallel if and only if the alternate exterior angles are congruent
Theorem 6.13 corresponding angle theorem
Two lines intersected by a transversal if and only if the corresponding angles are congruent
Theorem 6.14
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other also
Theorem 6.15
If two coplanar lines are perpendicular to the same line, then they are parallel to each other
Theorem 6.16
The sum of the measures of the angles of any triangle is 180
Theorem 6.17
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent
Theorem 6.18
The acute angles of a right triangle are complementary
Theorem 6.19 SAA congruence theorem
If two angles of a triangle and a side opposite one of the two angles are congruent to the corresponding angles and side of another triangle, then the two triangle, then the two triangles are congruent
Theorem 6.20 isosceles triangle theorem
In a isosceles triangle the two base angle are congruent
