Chapter 2 Study Guide Flashcards
Same side Interior angles
Two angles that are on the same side of the transversal between the two lines
Alternate interior angles
Angles in the inner side of the transversal but ok opposite sides
Same side exterior angles
Angles that are on the exterior of the parallel lines and the same side of the transversal
Alternate exterior angles
Angles on different sides of the transversal and exterior to the parallel lines
Corresponding angles
Angles of the same measure/ equal in size
Vertical angles
Angles that lie opposite to each other when two lines intersect
Linear pair
Adjacent angles that add up to 180 degrees / two angles that can be combined to make a line
Postulate 2-1: Same side interior angles postulate
If a transversal intersects two parallel lines, then the same side interior angles are supplementary
Theorem 2-1: Alternate interior angles theorem
If a transversal intersects two parallels, then alternate interior angles are congruent
Theorem 2-2: Corresponding Angles theorem
If a transversal intersects two parallel lines, then corresponding angles are congruent
Theorem 2-3: alternate exterior angles theorem
If a transversal line intersects two parallel lines, then alternate exterior angles are congruent
Theorem 2-4: Converse of the corresponding angles theorem
If two lines and a transversal form corresponding angles are congruent, then the lines are parallel
Theorem 2-5: Converse of the alternate Interior angles theorem
If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel
Theorem 2-6: Converse of the Same-Side Interior Angles Postulate
If two lines and a transversal form same side interior angles that are supplementary, then the lines are parallel
Theorem 2-7: Converse of the Alternate Exterior Angles Theorem
If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel
Theorem 2-8
If two lines are parallel to the same line, the. They are parallel to each other
Theorem 2-9
If two lines are perpendicular to the same line, then they are parallel to each other
Theorem 2-10
Through a point not on a line, there is one and only one parallel to the given line
Theorem 2-11: Triangle Angle Sum Theorem
The sum of the measures of all the angles in a triangle is equal to 180 degrees
Theorem 2-12: Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
Remote interior angles
The distant angles from the exterior angle being used
Theorem 2-13
Two non vertical lines are parallel if and only if their slopes are equal. Any two vertical lines are parallel
Theorem 2-14
Two non vertical lines are perpendicular if and only if the product of their slopes is -1. A vertical line and a horizontal line are perpendicular to each other.
If measure of angle 1 is equal to 71 find the measure of each angle: angle 5 ( HINT: Angles 1 and 5 are corresponding)
71 degrees
Use the Triangle Angle Sum Theorem: Find x and y. There are two triangles l. The first one has remote angles of 32 and 78 and then there’s. The second triangle has the remote interior angle of 57.
Steps to solve:
32+78+x = 180
180-110=x
X=70
angles QRT + angles TRS =180
Y+78= 180
180-78
Y= 102
Find x: The remote interior angles are 54 and 57, x is the exterior angle
Steps to solve:
54+57
=111
Find x: The remote interior angle is 49 and the exterior angle is 104, x is an interior angle
Steps to Solve:
104-49
=55
