Parallel Lines
The slope of parallel lines are always ______?
The slope of a perpendicular to a given line is the ___________ of the original line's slope.
What is the sum of the interior angles of a triangle?
180 Degrees
What is a convex polygon?
no diagonal with points outside the polygon
Has no interior angles greater than 180 degrees
Name the Theorem and Draw the Angles: If a transversal intersects 2 parallel lines then the corresponding angles are congruent
Corresponding angles postulate
What is the slope of a line that is parallel to
y=2/3x + 2?
2/3
What is the slope of a line that is perpendicular to
y=2/3x +2?
-3/2
Name and classify the 4 types of triangles based on angles
Acute: all angles are acute
Obtuse: one angle is obtuse
Right: one angle is a right angle
Equiangular: all angles are congruent
What is a concave polygon?
At least one diagonal with points outside of the polygon
Has one interior angle greater than 180 degrees
What type of theorem do you use to prove lines parallel?
Converse theorems
T/F: Vertical angles are always congruent
True
What kind of angle does a perpendicular line create?
Name and classify the 3 types of triangles based on side length.
Isosceles: 2 sides are congruent
Equilateral: all sides are congruent
Scalene: no sides are congruent
What is the polygon angle-sum theorem?
(n-2)180
Fill in the blank proof #2
vertical angles are congruent
corresponding angles are congruent
transitive property
T/F: Same side interior angles are always congruent.
False. Chance for 1/2 credit if you tell me what they are
T/F: If line A is perpendicular to line X, and line X is parallel to line Z, line A is also perpendicular to line Z.
True
What is the sum of all exterior angles of a triangle?
360 degrees
What is the sum of the interior angles of a pentagon?
540 degrees
Fill in the blank proof #1
definition of perpendicular
definition of a right angle
corresponding angles of parallel lines are congruent
substitution
definition of right angle
definition of perpendicular
Name all angle pairs of parallel lines cut by a transversal (5 total)
-vertical angles/linear pair
-consecutive interior/same side interior
-alternate interior
-alternate exterior
-corresponding angles
Determine whether the following lines are parallel, perpendicular, or neither
y=1/2 x + 2
y=2x +2
Perpendicular
What is the formula to find an exterior angle of a triangle?
Exterior angle = sum of the remote interior angles
(angles opposite the exterior angle)
What is a regular polygon?
A polygon that is both equilateral and equiangular
Suppose both pairs of opposite sides of a quadrilateral are parallel. Which angles of the quadrilateral must be supplemental?
Pairs of consecutive angles are supplementary because the sides of the quadrilateral are transversals and the interior angles are on the same side of the transversal.