Chapter 6 Vocabulary

Question 0

Theorem 6.2

Answer 0

Segment congruence is an equivalence relation

Question 1

Theorem 6.1

Congruent Segment Bisector Theorem

Answer 1

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

Question 2

Theorem 6.3

Answer 2

Supplements of congruent angles are congruent

Question 3

Theorem 6.4

Answer 3

Complements of congruent angles are congruent

Question 4

Theorem 6.5

Answer 4

Angle congruence is an equivalence relation

Question 5

Theorem 6.6

Adjacent Angle Sum Theorem

Answer 5

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

Question 6

Theorem 6.7

Adjacent Angle Portion Theorem

Answer 6

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

Question 7

Theorem 6.8

Congruent Angle Bisector Theorem

Answer 7

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

Question 8

Congruent circles

Answer 8

Circles with congruent radii

Question 9

Congruent polygons

Answer 9

Polygons with three properties

1) same number of sides
2) corresponding sides are congruent
3) corresponding angles are congruent

Question 10

Congruent Triangles

Answer 10

Triangles in which corresponding angles and corresponding side are congruent

Question 11

Theorem 6.9

Answer 11

Triangle congruence is na equivalence relation

Question 12

Theorem 6.10

Answer 12

Circle congruence is an equivalence relation

Question 13

Theorem 6.11

Answer 13

Polygon congruence is an equivalence relation

Question 14

Transversal

Answer 14

A line that intersects two or more distinct coplanar lines in tow or more distinct points

Question 15

Alternate interior angles

Answer 15

are angles such as 3 and 6, which are numbered on the opposite sides of the transversal and between the other two lines

Question 16

Alternate exterior angles

Answer 16

Angles such as 1 and 8; these angle numbers are on opposite sides of the transversal and outside the other two lines

Question 17

Corresponding Angles

Answer 17

Angles such as 2 and 6, these angle numbers are on the same side of the transversal and on the same side of their respective lines 3 and 7 form another pair of corresponding angles

Question 18

Postulate 6.1

Parallel Postulate

Answer 18

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

Question 19

Historic parallel postulate

Answer 19

Given a line and a point not on the line, there is exactly one line passing through the point that is parallel to the given line

Question 20

Theorem 6.12

Alternate Exterior Angle Theorem

Answer 20

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

Question 21

Theorem 6.13

Corresponding Angle Theorem

Answer 21

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

Question 22

Theorem 6.14

Answer 22

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

Question 23

Theorem 6.15

Answer 23

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

Question 24

Theorem 6.16

Answer 24

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

Question 25

Theorem 6.17

Answer 25

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

Question 26

Theorem 6.18

Answer 26

The acute angles of a right triangle are complementary

Question 27

Postulate 6.2

SAS Congruence Postulate

Answer 27

If two sides and an included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent

Question 28

Postulate 6.3

ASA Congruence Postulate

Answer 28

If two angles and an included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent

Question 29

Theorem 6.19

SAA Congruence Theorem

Answer 29

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

Question 30

Theorem 6.20

Isosceles Angle 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 triangle

Question 32

Theorem 6.22

Answer 32

A triangle is equilateral if and only if it is equiangular