table

glossary

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1.
30-60-90 Triangle Theorem: In a triangle whose angles have the measures 30, 60, and 90, the lengths of the sides opposite these angles can be represented by x,xrad3, and 2x.

2.
45-45-90 Triangle Theorem: In a triangle whose angles have the measures 45,45, and 90, the lengths of the sides opposite these angles can be represented by x, x, and xrad2.

3.
AA: If there exists a correspondence between the vertices of two triangles such that two angles of one triangle are congruent to the corresponding angles of the other, then the triangles are similar.

4.
Altitude on Hypotenuse Theorem: If an altitude is drawn to the hypotenuse of a right triangle, then 1) The triangles formed are similar to the given right triangle and to each other 2) The altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse 3) Either lef of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg.

5.
Angle Bisector Theorem: If a ray bisects an angle of triangle, it divides the opposite side into segments that are proportional to the adjacent sides.

6.
Angle-Arc Relationship: If two inscribed or tangent-chord angles intercept the same arc, then they are congruent.

7.
Angle-Arc Relationship: The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle is one-half the difference of the measures of the intercept arcs.

8.
Area of Circle: =pi(r^2)

9.
Area of Equilateral Triangle: =s^2/4(rad3)

10.
Area of Kite: =(1/2)d1d2

11.
Area of Parallelogram: =bh

12.
Area of Regular Polygon: =(1/2)ap

13.
Area of Sector: =(marc/360)pi(r^2)

14.
Area of Square: =s^2

15.
Area of Trapezoid: (1/2)h(b1+b2)

16.
Area of Trapezoid: =Mh

17.
Arithmetic Mean: An average where you take the sum of the figures, and dividing that by the number of figures you started with.

18.
Brahmagupta's Formula: =rad(s-a)(s-b)(s-c)(s-d)

19.
Central Angles - Arcs: If two central angles of a circle are congruent, then their intercepted arcs are congruent. (Or reverse)

20.
Central Angles - Chords: If two central angles of a circle are congruent, then their corresponding chords are congruent. (Or reverse)

21.
Chord-Chord Angle: The measure of a chord-chord angle is one-half the sum of the measure of the arcs intercepted by the chord-chord angle and its vertical angle.

22.
Chord-Chord Power Theorem: If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord.

23.
Chords - Arcs: If two chords of a circle are congruent then their corresponding arcs are congruent. (Or reverse)

24.
Chords of a Circle: If two chords are equidistant from the center, then they are congruent. (Or reverse)

25.
Circumference: =(pi)d

26.
Geometric Mean: Writing a proportion where the given numbers are the extremes and a variable as the extremes. (The answer is either positive or negative)

27.
Hero's Formula: =rads(s-a)(s-b)(s-c)

28.
Inscribed Angle: If the measure of an inscribed angle or a tangent-chord angle is one-half the measure of its intercepted arc.

29.
LA Cone: (pi)rl

30.
LA Cylinder: 2(pi)rh

31.
Length of Arc: =(marc/360)(pi)d

32.
Means-Extremes Product Theorem: In a proportion, the product of the means is equal to the product of the extremes. a/b=c/d - ad=bc (Similar to cross multiplying)

33.
Means-Extremes Ratio Theorem: If the product of a pair of nonzero numbers is equal to the product of another pair of nonzero numbers, then either pair of numbers may be made the extremes, and the other pair of means, of a proportion. pq=rs - p/r=s/q

34.
Measure of Median of Trapezoid: =1/2(b1+b2)

35.
Median of Triangle Theorem: A median of a triangle divides the triangle into two triangles with equal areas.

36.
Parallelogram in Circle: If a parallelogram is inscribed in a circle, it must be a rectangle.

37.
Perimeter-Side Ratio Theorem: The ratio of the perimeters of two similar polygons equals the ratio of any pair of corresponding sides.

38.
Proportionally: If three or more parallel lines are intersected by two transversals, the parallel lines divide the transversals proportionally.

39.
Pythagorean Theorem: If the square of the measure of one side of a triangle equals the sum of the squares of the measures of the other two sides, then the angle opposite the longest side is a right angle.

40.
Quadrilateral in Circle: If a quadrilateral is inscribed in a circle, its opposite angles are supplementary.

41.
Radius - Tangent Line: A tangent line is perpendicular to the radius drawn to the point of contact. (Or reverse)

42.
SAS~: If there exists a correspondance between the vertices of two triangles such that the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar.

43.
Secant-Secant Power Theorem: If two secant segments are drawn from an external point to a circle, then the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

44.
Side-Splitter: If a line is parallel to one side of a triangle and intersects the other two sides, it divides those to sides proportionally.

45.
Similar Figures Theorem: A1/A2=(S1/S2)^2

46.
Similar Polygons: The ratios of the measures of the corresponding sides are equal. Corresponding angles are congruent.

47.
Slope-Intercept: y=mx+b

48.
SSS~: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of the corresponding sides are equal, then the triangles are similar.

49.
TA Sphere: 4(pi)r^2

50.
Tangent-Secant Power Theorem: If a tangent segment and a secant segment are drawn from an external point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part.

51.
Three Trigonometric Ratios: SOH CAH TOA

52.
Two-Tangent Theorem: If two tangent segments are drawn to a circle from and external point, then those segments are congruent.

53.
Volume Cone: (1/3)(pi)(r^2)(h)

54.
Volume Cylinder: (pi)r^2h

55.
Volume Prism: Bh

56.
Volume Prism/Cylinder: (area of cross section)h

57.
Volume Pyramid: (1/3)Bh

58.
Volume Rectangular Box: lwh

59.
Volume Sphere: (4/3)(pi)(r^3)

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