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### 43 Cards in this Set

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