Theorems

Question 0

Theorem 4.2

Answer 0

If two angles are adjacent and supplementary, then they form a linear pair

Question 1

Theorem 4.1

Answer 1

All angles are congruent

Question 2

Theorem 4.3

Answer 2

Angles that form a linear pair are supplementary

Question 3

Theorem 4.4

Answer 3

If one angle of a linear pair is a right angle, then the other angle is also a right angle

Question 4

Theorem 4.5 VERTICAL ANGLE THEOREM

Answer 4

Vertical angles are congruent

Question 5

Theorem 4.6

Answer 5

Congruent supplementary angles are right angles

Question 6

Theorem 4.7 ANGLE BISECTOR THEOREM

Answer 6

If ->AB bisects /_ CAD, then m/_CAB=1/2m/_CAD

Question 7

Theorem 5.1

Answer 7

The conditional p->q, is equivalent to the disjunction ~p or q

Question 8

Theorem 5.2 CONTRAPOSITVE RULE

Answer 8

A conditional statement is equivalent to its contrapositve. In other words, p->q is equivalent to ~q->~p

Question 11

Theorem 6.1 CONGRUENT SEGMENT BISECTOR THEOREM

Answer 11

If two congruent segments are bisected, then the four resulting segments are congruent

Question 12

Theorem 6.2

Answer 12

Segment congruence is an equivalence relation

Question 13

Theorem 6.3

Answer 13

Supplements of congruent angles are congruent

Question 14

Theorem 6.4

Answer 14

Complements of congruent angles are congruent

Question 15

Theorem 6.5

Answer 15

Angle congruence is an equivalence relation

Question 16

Theorem 6.6 ADJACENT ANGLE SUM THEOREM

Answer 16

If two adjacent angles are congruent to another pair of adjacent angles formed are congruent

Question 17

Theorem 6.7 ADJACENT ANGLE PORTION THEOREM

Answer 17

If two angles, one in each of two pairs of adjacent angles, are congruent, and the larger angles formed are also congruent, then the other two angles are congruent with

Question 18

Theorem 6.8 CONGRUENT ANGLE BISECTOR THEOREM

Answer 18

If two congruent angles are bisected, the four resulting angles are congruent

Question 19

Theorem 6.9

Answer 19

Triangle congruence is an equivalence relation

Question 20

Theorem 6.10

Answer 20

Circle congruence is an equivalence relation

Question 21

Theorem 6.11

Answer 21

Polygon congruence is an equivalence relation

Question 22

Theorem 6.12 ALTERNATE EXTERIOR ANGLE THEOREM

Answer 22

Two line intersected by a transversal are parallel of and only if the alternate exterior angles are congruent.

Question 23

Theorem 6.13 CORRESPONDING ANGLE THEOREM

Answer 23

Two lines intersected by a transversal are parallel if and only if the corresponding angles are congruent.

Question 24

Theorem 6.14

Answer 24

If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other one also.

Question 25

Theorem 6.15

Answer 25

If two coplanar lines are perpendicular to the same line, then they are parallel to each other.

Question 26

Theorem 6.16

Answer 26

The sum of the measure of the angles of any triangle is 180°

Question 27

Theorem 6.17

Answer 27

If two of one triangle are congruent to two angles of another triangle, then the third angles are also congruent

Question 28

Theorem 6.18

Answer 28

The acute angles of a right triangle are complementary

Question 29

Theorem 6.19 SAA CONGRUENCE THEOREM

Answer 29

If two angles of a triangle and a side opposite one of the two angles are congruent to the corresponding angles and a side of another triangle, then the two triangles are congruent.

Question 30

Theorem 6.20 ISOSCELES TRIANGLE THEOREM

Answer 30

In an isosceles triangle the two base angles are congruent.

Question 31

Theorem 6.21

Answer 31

If two angles of a triangle are congruent, then the sides opposite those angles are congruent, and the triangle is an isosceles.

Question 32

Theorem 6.22

Answer 32

A triangle is equilateral if and only if it is equiangular.