Chapter 6 Vocabulary Flashcards
Theorem 6.2
Segment congruence is an equivalence relation
Theorem 6.1
Congruent Segment Bisector Theorem
If two congruent segments are bisected, then four resulting segments are congruent
Theorem 6.3
Supplements of congruent angles are congruent
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 of two pairs of adjacent angles, are congruent, and the larger angles formed are also congruent, then the two other pairs are congruent
Theorem 6.8
Congruent Angle Bisector Theorem
If two congruent angles are bisected, the four resulting angles are congruent
Congruent circles
Circles with congruent radii
Congruent polygons
Polygons with three properties
1) same number of sides
2) corresponding sides are congruent
3) corresponding angles are congruent
Congruent Triangles
Triangles in which corresponding angles and corresponding side are congruent
Theorem 6.9
Triangle congruence is na equivalence relation
Theorem 6.10
Circle congruence is an equivalence relation
Theorem 6.11
Polygon congruence is an equivalence relation
Transversal
A line that intersects two or more distinct coplanar lines in tow or more distinct points
Alternate interior angles
are angles such as 3 and 6, which are numbered on the opposite sides of the transversal and between the other two lines
Alternate exterior angles
Angles such as 1 and 8; these angle numbers are on opposite sides of the transversal and outside the other two lines
Corresponding Angles
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
Postulate 6.1
Parallel Postulate
Two lines intersected by a transversal are parallel if and only if the alternate interior angles are congruent
Historic parallel postulate
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
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 are parallel if and only if the corresponding angles are congruent
Theorem 6.14
If a transversal is perpendicular to one of the tow 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
Postulate 6.2
SAS Congruence Postulate
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
Postulate 6.3
ASA Congruence Postulate
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
Theorem 6.19
SAA Congruence Theorem
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
Theorem 6.20
Isosceles Angle Theorem
In an isosceles triangle the two base angles are congruent
Theorem 6.21
If two angles of a triangle are congruent, then the sides opposite those angles are congruent, and the triangle is an isosceles triangle
Theorem 6.22
A triangle is equilateral if and only if it is equiangular
