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 right 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 5.1

Answer 6

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

Question 7

Theorem 5.2

Contrapositive rule

Answer 7

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

Question 8

Theorem 6.1 congruent segment bisector theorem

Answer 8

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

Question 9

Theorem 6.2

Answer 9

Segment congruence is an equivalence relation

Question 10

Theorem 6.4

Answer 10

Complements of congruent Angles are congruent

Question 11

Theorem 6.5

Answer 11

Angle congruence is an equivalence relation

Question 12

Theorem 6.6 adjacent angle sum theorem

Answer 12

If two adjacent angles are congruent to another pair of adjacent angles, then the larger angles formed are congruent

Question 13

Theorem 6.7 adjacent angle portion theorem.

Answer 13

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

Question 14

Theorem 6.8 congruent angle bisector theorem.

Answer 14

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

Question 15

Theorem 6.9

Answer 15

Triangle congruence is an equivalence relation

Question 16

Theorem 6.10

Answer 16

Circle congruence is an equivalence relation

Question 17

Theorem 6.11

Answer 17

Polygon congruence is an equivalence relation

Question 18

Theorem 6.12 alternate exterior angle theorem

Answer 18

Two lines intersected by a transversal are parallel if and only if the alternate exterior angles are congruent

Question 19

Theorem 6.13 corresponding angle theorem

Answer 19

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

Question 20

Theorem 6.14

Answer 20

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

Question 21

Theorem 6.15

Answer 21

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

Question 22

Theorem 6.16

Answer 22

The sum of the measures of the angles of any triangle is 180

Question 23

Theorem 6.17

Answer 23

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

Question 24

Theorem 6.18

Answer 24

The acute angles of a right triangle are complementary

Question 25

Theorem 6.19 SAA congruence theorem

Answer 25

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

Question 26

Theorem 6.20 isosceles triangle theorem

Answer 26

In a isosceles triangle the two base angle are congruent