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43 Cards in this Set
- Front
- Back
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Triangle Sum Conjecture
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sum of the three angles equals 180 degrees
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The properties of Isosceles triangles
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two sides are congruent, base angles are congruent
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triangle inequalities
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the sum of two sides is greater than the third side
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shortcuts to congruent triangles
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SSS, SAS, AAS, ASA, SSA,
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CPCTC
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use it to prove shapes are congruent
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Polygon interior sum conjecture
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180(n-2)
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exterior angle sum
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720
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properties of a parallelagram
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opposite sides are congruent and parallel
consecutive angles are supplementary diagonals bisect |
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Rectangle properties
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all angles are right
opposite sides are congruent and parallel diagonals are congruent and bisect e/o |
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Rhombus properties
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all sides are congruent
diagonals bisect e/o and the angles |
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square properties
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all sides are congruent
all 90 degree angles diagonals are congruent, bisect e/o and are angle bisectors |
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kite properties
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consecutive sides are congruent
nonvertex angles are congruent diagonals bisect the vertex angles diagonal bisec the nonvertex diagonal |
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trapezoid properties
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parallel bases
consecutive angles are supplementary |
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Isos. trapezoid
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bases are parallel
other sides are congruent base angles are congruent |
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triangle midsegment
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midsegment parallel to the third sides, divide triangle into 4 congruent triangles
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trapezoid midsegment
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midsegment parallel to all bases
average of the bases |
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Congruent circles
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circles that have the same shape and size
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concentric circles
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a circle inside other circles
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radius
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the segment connecting the center to any point of the circle
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chord
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a segment from one point on a circle to the other not including the center
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diameter
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a segment containing one point of a circle to the other containing the center
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tangent
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a line that touches on point on the circle
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minor arc
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a part of the circle arc that is less a semicircle
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major arc
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a part of the circle more than a semicircle
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semicircle
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the arc of a cirle that takes up half of the circle
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Chord Properties
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-two chords congruent the central angles are congruent
-two chords are congruent, two arcs are congruent -perpendicular from center to chord bisects it -two chords are congruent, distance from center is congruent -perpendicular of the chord bisects the angle; |
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Tangent Properties
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-the radius that intersects a tangent is perpendicular
-two tangents that intersect at a point are congruent -can be internally and externally tangent to e/o -circles can have up to four tangents- external and internal |
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arc and angle relationships
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-Inscribed angle is half the measure of the arc
-Two or more inscribed angles that are intercepting the same arc are congruent -Angles inscribed in semicircle are 90 degrees |
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circumference vs area
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-Circumference divided by diameter equals pi
-Area= pi r^2 |
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The Pythagorean Theorem
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a^2 + b^2 = c^2
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Pythagorean Theorem triples
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nice numbers that work in the Pythagorean theorem
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45-45-90
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a= a
b= a c= a sq. rt. 2 |
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30-60-90
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a= a
b= a sq. rt. 3 c= 2a |
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Distance equation
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sqroot(x1-x2)^2 + (y1 + y2)^2
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Simularity shortcuts
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AA
SAS SSS |
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Geometric means
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a/x= c/a
b/y= c/b h/x= y/h |
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porportional parts
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abc is simular to def
ab/de= bc/ef = ca/fd |
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scale factor in terms of...
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sf
area (sf)^2 surface area(sf)^2 volume (sf)^3 mass(sf)^3 |
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area
Prism Sphere Cone Pyramid Cylinder |
Prism- base times height
Sphere- 4/3 pi r^3 Cone- 1/3 pi r^2 times height Pyramid- 1/3 bh Cylinder- bh |
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Centroid
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medians
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Incenter
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angle bisectors
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circumcenter
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perpendicular bisectors
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orthocenter
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altitudes
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