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Geometry Extended Midterm Review
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Terms in this set (60)
Perpendicular Lines
Two lines that intersect to form a right angle.
Parallel Lines
Two coplanar lines that do not intersect.
Theorem
A statement that you prove using logical reasoning.
Midpoint
A point that divides a segment into two congruent parts.
Segment Bisector
A line that passes through the midpoint of a segment.
Perpendicular Bisector
A line that bisects a segment and is also perpendicular to it.
Angle Bisector
A ray that divides an angle into two congruent parts.
Angle Addition Postulate
part of the angle + part of the angle = total angle
Complementary Angles
Two angles that make 90 degrees.
Supplementary Angles
Two angles that make 180 degrees.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Right Angle
An angle whose measure is 90 degrees.
Acute Angle
An angle whose measure is less than 90 degrees.
Obtuse Angle
An angle whose measure is greater than 90 degrees an less than 180.
Straight Angle
An angle whose measure is 180 degrees.
Collinear
Points that lie on the same line.
Coplanar
Points that lie on the same plane.
points
shown as dots, have no size, named by capital letters such as A or X
lines
have no thickness, are perfectly straight, and extend forever, can be named by two points on the line with line drawn above or by a single lowercase letter
planes
extend indefinitely in all directions along a flat surface, named by three non collinear points that lie in the plane or by a script capital letter
segment
is part of a line that begins at one endpoint and ends at another endpoint.
ray
part of a line that starts at a point and extends infinitely in one direction
angle
a figure formed by two rays with a common endpoint
vertex
common endpoint of two rays
alternate exterior angles
Two nonadjacent exterior angles that lie on opposite sides of a transversal. Angles are congruent
alternate interior angles
Two nonadjacent interior angles that lie on opposite sides of a transversal. Angles are congruent
corresponding angles
Two angles that are in the same spot at different locations of the transversal. Angles are congruent
polygon
A closed plane figure formed from three or more segments such that each segment intersects exactly two other segments, one at each endpoint and no two segments with a common endpoint are collinear.
parallelogram
A quadrilateral with two pairs of parallel sides. Opposites angles are congruent. Opposite sides are congruent. Diagonals bisect each other
quadrilateral
A polygon with four sides
rectangle
A quadrilateral with four right angles. Diagonals are congruent
regular polygon
A polygon that has all equal angles and all equal sides
rhombus
A quadrilateral with four congruent sides. Does NOT have a right angle. Diagonals are Perpendicular
same-side interior angles
Interior angles that lie on the same-side of a transversal. Angles are supplementary
square
A quadrilateral with four congruent sides and four right angles.
transversal
A line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point.
trapezoid
A quadrilateral with one and only one pair of parallel sides.
Triangle Sum Theorem
The sum of the measures of the angles of a triangle is 180˚.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Sum of the Interior Angles of a Polygon
The sum of the measures of the interior angles of a polygon with n sides is given by (n-2)180˚.
Sum of the Exterior Angles of a Polygon
The sum of the measures of the exterior angles of a polygon is 360˚.
Parallel Lines Theorem
In a coordinate plane, two nonvertical lines are parllel if and only if they have the same slope.
Perpendicular Lines Theorem
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
vertical angles
two non-adjacent (opposite) angles formed by two intersecting lines
adjacent angles
angles that have a common vertex and a common side, but no common interior points
congruent polygons
all corresponding angles and all corresponding sides congruent
SSS (side-side-side) postulate
If three sides in one triangle are congruent to three sides in another triangle, then the triangles are congruent
SAS (side-angle-side) postulate
If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them in another triangle, then the triangles are congruent
ASA (angle-side-angle) postulate
If 2 angles and the side between them in one triangle are congruent to 2 angles and the side between them in another triangle, then the triangles are congruent
AAS (angle-angle-side) theorem
If 2 angles and a side that is not between them in one triangle are congruent to the corresponding 2 angles and the side not between them in another triangle, then the triangles are congruent
HL (Hypotenuse-leg) theorem
IF the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and the corresponding leg in another right triangle, then the two triangles are congruent.
isosceles triangle
A triangle with at least 2 congruent sides and 2 congruent angles.
equilateral triangle
A special type of triangle in which all 3 sides of the triangle are congruent and 3 equal 60 degree angles
Triangle Inequality Postulate
The sum of the lengths of any 2 sides of a triangle is larger than the length of the other (3rd) side.
Pythagorean Theorem
a²+b²=c²
Area of a Parallelogram
A=bh
Area of a Trapezoid
A = ½ h (b₁ + b₂)
Area of a Circle
A=πr²
Circumference of a Circle
C = 2πr
Area of a Triangle
A=1/2bh
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