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Definition
| an angle whose measure is 90 degrees |
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| an angle whose measure is more than 0 degrees and less than 90 |
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| an angle whose measure is less than 180 degrees but more than 90 |
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| an angle whose measure is 180 degrees |
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| by a point on one ray, the vertex, and a point on the other ray
ex: |
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Definition
| always add up to 180 degrees |
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| angles whose meausure adds up to 180 degrees |
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| angles whose measure adds up to 90 degrees |
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^
II | I
<-------|------>
III | IV
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Makes a "C" when you connect them numerically |
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Definition
a location that's infinitely small and is labeled with a capital letter
ex: A(6,9) |
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<----> a set of connected points named by the points ex: <-->
AB |
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| two lines that intersect at 4 90 degree angles |
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| points/lines that lie on the same plane |
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| 2 or more objects that never intersect |
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| _________________________________________
V(X1-X2)2 + (Y1-Y2)2 |
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Definition
part of a line between 2 points
Ex: ____
AB |
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| point that is an equal distance from both points
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((X1+X2/2),(Y1+Y2/2)) |
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2 noncollinear rays connected by a common endpoint
Ex: ^
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exterior| interior
-------> |
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Definition
part of a line with one endpoint
.___>
AB |
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Definition
| the common endpoint of 2 rays, forming an angle |
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make a straight angle
<--------.--------> |
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| angles that are right next to each other (touching) in the same plane with a common vertex |
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| formed by 2 intersecting lines; going in opposite directions |
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| adjacent angles whose noncommon sides are opposite rays; form a straight angle |
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| a statement based on several observations that may or may not be true |
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| a statement used to prove somthing wrong |
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| mathematical statement which can be proven true |
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| axiom; a mathematical statement we assume to be true but cannot be proven. |
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| two lines that do not intersect and are not coplanar |
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| a line that intersects 2 or more lines in a plane at different points |
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| alternate interior angles |
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Definition
^
5|7
<-------|---------> angles: 1, 4, 2, 6
1 |4 (adjacent angles interior)
6 |2
<-------|--------->
8 |3 |
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Term
| consecutive interior angles |
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Definition
^
5|7
<-------|---------> angles: 1, 5, 8, 6
1 |4 (adjacent angles on same
| side of transversal)
6 |2
<-------|--------->
8 |3 |
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Term
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Definition
^
5|7
<-------|---------> angles: 1, 8, 5, 6
1 |4 (makes an "F")
6 |2
<-------|--------->
8 |3 |
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Term
| alternate exterior angles |
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Definition
^
5|7
<-------|---------> angles: 5, 8, 7, 3
1 |4 (opposite ends exterior)
6 |2
<-------|--------->
8 |3 |
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Term
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Definition
| parallel lines have same slope.
perpendicular lines have opposite recyprocal slope.
horizontal line = zero slope
vertical line = no slope (no way ur surviving)
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m=(Y1-Y2)/(X1-X2) |
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| The distance from a line to a point not on the line |
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| the length of the segment perpendicular to the line from the point....shortest route |
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| If the transversal is perpendicular to one of the parallel lines |
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Definition
| then it is perpendicular to the other(s) |
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Definition
| all 3 sides of a triangle are congruent to each other |
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| at least 2 sides of a triangle congruent to each other |
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| all sides have different measurements |
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| a triangle w/ one 90 degree angle |
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| all 3 angles are > 90 degrees |
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| has only one obtuse angle |
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| in an isosceles triangle/trapezoid are olways congruent |
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| triangles with corresponding parts congruent |
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| If 3 sides of one triangle have the same measurement as 3 sides of another triangle, then the 2 triangles are congruent. |
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| If 2 sides of one triangle with a side between two angles corresponds to the side and angles of another triangle, then the 2 triangles are congruent. |
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Definition
| If 2 sides of one triangle and the included angle correspond to another triangle, then the 2 triangles are congruent. |
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| If 2 angles of one triangle with a side after correspond to another triangle's, then the 2 triangles are congruent. |
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Definition
| If a=b and b=c, then c=a. |
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Definition
| any line segment drawn from any vertex perpendicular to the opposite side or the extension of that side; in a right triangle the legs are altitudes |
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Definition
| line segment that extends from any vertex to the midpoint of the opposite side |
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| any line segment that cuts an angle into 2 congruent parts |
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Definition
| In a right triangle, if the hypotenuse and an angle correspond to the hypotenuse and angle of another right triangle, then they are congruent. |
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Definition
| In a right triangle, if a leg and an angle correspond to a leg and angle of another right triangle, then they are congruent. |
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Definition
| In a right triangle, if 2 legs correspond to 2 legs of another right triangle, then they are congruent. |
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Term
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Definition
| In a right triangle, if the hypotenuse and a leg correspond to the hypotenuse and leg of another right triangle, then they are congruent. |
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Term
| Angles and Sides Theorem: angle measures and side measures and adding up |
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Definition
short leg across from short angle; long leg across from big angle
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Any 2 sides in a triangle have to add up to be more than te 3rd side |
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Definition
opposite sides congruent
opposite sides parallel
opposite angles congruemt
consecutive angles are supplementary
diagonals bisect each other |
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Definition
opposite sides congruent
opposite sides parallel
opposite angles congruemt
diagonals bisect each other
diagonals bisect opposite angles
diagonals are perpendicular |
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Definition
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Term
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Definition
Hyp=2 x short leg
long leg=short leg x root 3 |
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Definition
legs congruent
hyp=leg x square root 2
leg=hypotenuse
leg x root 2= leg x 2 |
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Term
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Definition
| piece of hyp x alt
alt other hyp piece |
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Term
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Definition
| a line segment from the center of the circle to any point on the cirlce; all radii are congruent in one circle |
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Definition
| line segment, which joins any 2 points on the circle |
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Definition
| a line that contains a chord; intersects the circle at 2 points |
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| a line that intersects the circle at one point |
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| Formula to Find Circle Radius and Center |
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Definition
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Definition
| part of a circle between any 2 pts....shortest route possible |
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Definition
| part of a circle between any 2 pts....longest route possible |
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Definition
| an arc half as big as the circumference of a circle |
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| made by 2 radii; big as its arc |
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Definition
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| Chords an equal distance away from the center |
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Definition
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| If a chord is perpendicular to a radius, |
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Definition
| then the chord is bisected |
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Term
| If a radius and a tangent intersect, |
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Definition
| then they are perpendicular to each other |
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Term
| If there are 2 tangents from the same exterior point, |
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Definition
| then they are congruent to each other |
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Term
| If lines intersect inside a circle: formula for arc measures |
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Definition
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Term
| If lines intersect outside the circle: formula for arc measure |
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Definition
| (far arc[from vertex]-close arc[from vertex])/2 |
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Term
If 2 chords intersect in a circle,
or
If 2 secants intersect at an ext. point,
or
If a tangent and a secant, |
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Definition
| then the products of the measures of the segments of the chords are equal
Ex:chord 1 x rest of chord 1= chord 2 x the rest of chord 2
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whole secant x exterior secant=other whole secant x other exterior secant
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tangent2=whole secant x exterior secant |
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