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Math 10R Definitions, Theorems, Postulates
Postulates are accepted without proof.
Definitions describe a term and are reversible.
Theorems can be proven.
P2: SEGMENT ADDITION POSTULATE If AB = DE and BC = EF then AC = DF
(seg. add. post.)
Def: The midpoint of a segment is the point that divides a segment into two congruent
segments. (midpt ↔ 2  seg)
Def: A segment bisector is a point, ray, line, segment or plane that intersects a
segment at its midpoint. (seg bisector ↔ 2  seg)
Def: Congruent segments are segments that have equal lengths. (  seg are =)
Def: Opposite rays are 2 collinear rays that have a common endpoint and
extend in opposite directions.
P4: ANGLE ADDITION POSTULATE If <ABC  <DEF and <CBN  <FEM then
<ABN  <DEM (angle add. post.)
Def: A right angle is an angle with measure equal to 90º. (rt <’s = 900)
Def: Congruent angles are angles that have equal measure. (  <’s are =)
Def: An angle bisector is a ray that divides an angle into two congruent angles.
( bisector ↔ 2  ’s)
Def: A linear pair are 2 adjacent angles that form a straight line.
P12: Linear Pair Postulate: If two angles form a linear pair, then they are
supplementary.
(lin. pair → supp s)
Def: Supplementary angles are 2 angles whose measures have the sum 180º.
Def: Complementary angles are 2 angles whose measures have the sum 90º.
Def: Perpendicular lines are two lines that intersect to form a right angle.
(  lines ↔ rt s)
*Draw pictures for P5 – P11.
P5: Through any 2 points there exists exactly one line.
P6: A line contains at least two points.
P7: If two lines intersect, then their intersection is exactly one point.
P8: Through any 3 non collinear points there exists exactly one plane.
P9: A plane contains at least 3 non collinear points.
P10: If 2 points lie in a plane, then the line containing them lies in the plane.
P11: If 2 planes intersect, then their intersection is a line.
P13: Parallel Postulate If there is a line and a point not on the line, then there is
exactly one line through the point parallel to the given line.
P14: Perpendicular Postulate If there is a line and a point not on the line, then
there is exactly one line through the point perpendicular to the given line.
Th 2-1: Properties of Segment Congruence:
Reflexive Property of Congruence ____________________________
Symmetric Property of Congruence ___________________________
Transitive Property of Congruence ____________________________
Th 2-2: Properties of Angles Congruence:
Reflexive Property of Congruence ____________________________
Symmetric Property of Congruence ___________________________
Transitive Property of Congruence____________________________
Algebraic Properties of Equality:
Addition Property of Equality ____________________________________
Subtraction Property of Equality __________________________________
Multiplication Property of Equality _________________________________
Division Property of Equality _____________________________________
Substitution Property of Equality __________________________________
Distributive Property of Equality___________________________________
Simplification Property of Equality _________________________________
Properties of Equality
Reflexive Property of Equality ____________________________________
Symmetric Property of Equality ___________________________________
Transitive Property of Equality ____________________________________
Th 2-3: Right Angles Congruence Theorem - All right angles are congruent.
(rt s →  s)
Th 2-4: Congruent Supplements Theorem - If two angles are supplementary
to the same angle (or congruent angles) then the two angles are congruent.
(s supp to the same or  s are  )
Th 2-5: Congruent Complements Theorem - If two angles are complementary
to the same angle (or congruent angles) then the two angles are congruent.
(s comp to the same or  s are  )
Th (Not in book): Angles congruent to the same angle or to congruent angles are
congruent. (<’s  to the same or  <’s are  )
Th 2-6: Vertical Angles Congruence Theorem - Vertical angles are congruent.
(vert <’s →  <’s)
Def: Parallel lines are two lines in the same plane that do not intersect.
Def: Skew lines are lines that do not intersect and are not coplanar.
Def: A transversal is a line that intersects two or more coplanar lines at different
points.
P15 - Corresponding Angles Postulate - If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are congruent. (For use with P15 and 16:
lines ↔  corr s)
Th 3-1,2,3: If two parallel lines are cut by a transversal, then the pairs of
-1: alternate interior angles are congruent.
(For use with 3-1 and 3-4: lines ↔  alt int s)
-2: alternate exterior angles are congruent.
(For use with 3-2 and 3-5: lines ↔  alt ext s)
-3: consecutive interior angles are supplementary.
(For use with 3-3 and 3-6: lines ↔ consec int s are supp)
Th 3-7: Transitive Property of Parallel lines - If two lines are parallel to the same line
then they are parallel to each other. (transitive prop. of ll lines)
Th 3-11: Perpendicular Transversal Theorem - If a transversal is
perpendicular to one of two parallel lines, then it is perpendicular to the other.
(Transversal  thm)
Th 3-12: Lines Perpendicular to a Transversal Theorem - In a plane, if two
lines are perpendicular to the same line, then they are parallel to each other.
(lines  to same line are ll)
P16 - Corresponding Angles Converse If two lines are cut by a transversal so
the corresponding angles are congruent, then the lines are parallel.
Th 3-4,5,6: If two parallel lines are cut by a transversal, so the
-4: alternate interior angles are congruent,
-5: alternate exterior angles are congruent,
-6: consecutive interior angles are supplementary,
then the lines are parallel.
Def: The slope of a non-vertical line is the ratio of the vertical change (the rise)
y y
to the horizontal change (the run) between any two points on the line. m  2 1
x2  x1
P17: Slopes of parallel lines In a coordinate plane, two non vertical lines are
parallel if and only if they have the same slope. Any two non vertical lines are
parallel. (II lines have = slope)
P18: Slopes of Perpendicular lines In a coordinate plane, two non vertical
lines are perpendicular if and only if the product of their slopes is -1 (or slopes
are negative reciprocals). Horizontal lines are perpendicular to vertical lines.
(  lines have neg. recip. slopes)
Def: The distance from a point to a line is the length of the perpendicular
segment from the point to the line. (The shortest distance)
Def: An acute triangle is a triangle with 3 acute angles.
Def: An obtuse triangle is a triangle with one obtuse angle.
Def: A right triangle is a triangle with one right angle.
Def: An equiangular triangle is a triangle with three congruent (equal) angles.
Def: A scalene triangle is a triangle with no congruent sides.
Def: An isosceles triangle is a triangle with at least two congruent sides.
(isos ∆ ↔ ∆ w/ 2  sides & 2  base s)
Def: An equilateral triangle is a triangle with three congruent sides.
(equil ∆ ↔ ∆ w/ 3  sides & 3  s)
Th 4-1: Triangle Sum Theorem: The sum of the measures of the interior angles
of a triangle is 180º. (s of ∆ = 180)
Th 4-2: Exterior Angle Theorem The measure of an exterior angle of a triangle
is equal to the sum of the measures of the two non-adjacent interior angles.
(ext  of ∆ = sum of 2 remote int. s)
Th 4-3: Third Angles Theorem If two angles of one triangle are congruent to
two angles of another triangle, then the third angles are also congruent.
(third  th)
Def: Two triangles are congruent if and only if their corresponding parts are
congruent.
Th: Corresponding parts of congruent triangles are congruent. (CPCTC)
Th 4-4: Properties of Triangle Congruence Triangle congruence is reflexive,
symmetric and transitive.
P19 - Side-Side-Side (SSS) Congruence Postulate - If three sides of one triangle are
congruent to three sides of a second triangle, then the two triangles are congruent.
(SSS  SSS)
P20 - Side-Angle-Side (SAS) Congruence Postulate - If two sides and the
included angle of one triangle are congruent to two sides and the included angle
of a second triangle, then the two triangles are congruent. (SAS  SAS)
P21 - Angle-Side-Angle (ASA) Congruence Postulate - If two angles and the
included side of one triangle are congruent to two angles and the included side of a
second triangle, then the two triangles are congruent. (ASA  ASA)
Th 4-5: Hypotenuse-Leg (HL) Congruence Postulate - If the hypotenuse and
a leg of a right triangle are congruent to the hypotenuse and a leg of a second
right triangle, then the two triangles are congruent. (HL (rt ∆)  HL (rt ∆))
Th 4-6: Angle-Angle-Side (AAS) Congruence Postulate - If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent. (AAS  AAS)
Th 4-7: Base Angles Theorem If two sides of a triangle are congruent , then the
angles opposite them are congruent. (2  sides in a ∆ → s opp them are  )
Corollary: If a triangle is equilateral, then it is equiangular.
Th 4-8: Converse of the Base Angles Thm If two angles of a triangle are
congruent, then the sides opposite them are congruent.
(2  s in a ∆ → sides opp them are  )
Corollary: If a triangle is equiangular, then it is equilateral.
Def: The Midsegment of a triangle is a segment that connects the midpoints of
two sides of the triangle.
Th 5-1: Midsegment Thm The segment connecting the midpoints of two sides
of a triangle is parallel to the third side and is half as long as that side.
Def: The Perpendicular Bisector of a segment is a segment, ray, line or plane that is
perpendicular to a segment at its midpoint.
(  bisector →  lines) and (  bisector → midpt)
Def: A Median of a triangle is a segment from one vertex of a triangle to the
midpoint of the opposite side. (median → midpt)
Def: An Altitude of a triangle is the perpendicular segment from one vertex of
the triangle to the opposite side or to the line that contains the opposite side.
Def: The Circumcenter of a Triangle The point of concurrency of the three
perpendicular bisectors of a triangle.
Def: The Incenter of a Triangle The point of concurrency of the three angle
bisectors of a triangle.
Def: The Centroid of a Triangle The point of concurrency of the three medians
of a triangle.
Def: The Orthocenter of a Triangle The point at which the lines containing the
three altitudes of a triangle intersect.
Th 5-2: Perpendicular Bisector Thm If a point is on the perpendicular bisector
of a segment, then it is equidistant from the endpoints of the segment.
(pt on  bisector ↔ pt is equidistant from endpts of seg)
Th 5-3: Converse of Perp Bisector Thm If a point is equidistant from the
endpoints of a segment, then it is on the perpendicular bisector of the segment.
(use above shortcut for Th 5 -2 as well)
Th 5-4: Concurrency of Perpendicular Bisectors Thm The perpendicular bisectors
of a triangle intersect at a point that is equidistant from the vertices of the triangle.
(pt of concurrency of perp bisectors intersect at a pt equidistant from all vertices)
Th 5-5: Angle Bisector Thm - If a point is on the bisector of an angle, then it is
equidistant from the two sides of an angle. (pt on  bisector ↔ pt is equidistant from 2
sides of )
Th 5-6: Converse of the Angle Bisector Thm If a point is in the interior of an
angle and is equidistant from the sides of an angle, then it lies on the bisector of
the angle. (use above shortcut for Th 5-6 as well)
Th 5-7: Concurrency of Angle Bisectors of a Triangle The angle bisectors of a
triangle intersect at a point that is equidistant from the sides of the triangle.
(pt of concurrency of  bisectors intersect at a pt equidistant from all sides)
Th 5-8: Concurrency of Medians of a Triangle The medians of a triangle intersect at
a point that is two-thirds of the distance from each vertex to the midpoint of the opposite
side. (pt of concurrency of medians intersect at a pt 2/3 the distance from vertices)
Th 5-9: Concurrency of Altitudes of a Triangle The Lines containing the
altitudes of a triangle are concurrent.
Def: Inequality: For any real numbers a nd b, a > b if and only if there is a
positive number c such that a = b + c.
Thm (Not in Book): The measure of an exterior angle of a triangle is greater
than the measure of either non-adjacent interior angle.
(Recall Exterior Angle Theorem: 4.2)
Th 5-10: If one side of a ∆ is longer than another side, then the angle opposite
the longer side is larger than the angle opposite the shorter side.
(In a ∆, the greater  is opp the longer side)
Th 5-11: If one  of a ∆ is larger than another , then the side opposite the larger 
is longer than the side opposite the smaller angle.
(In a ∆, the longer side is opp the greater  )
Th 5-12: Triangle Inequality Thm The sum of the lengths of any two sides of a
triangle is greater than the length of the third side. (the sum of the lengths of
any 2 sides of a ∆ is > the length of the 3rd side)
Th 5-13. Hinge Theorem: If two sides of one triangle are congruent to two
sides of another triangle, and the included angle of the first is larger than the
included angle of the second, then the third side of the first is longer than the
third side of the second.
Th 5-14: Converse of the Hinge Theorem If two sides of one triangle are
congruent to two sides of another triangle, and the third side of the first is longer
than the third side of the second, then the included angle of the first is larger than
the included angle of the second.
Th (not in book) The exterior angle of a triangle is greater than either
nonadjacent interior angle (ext  of ∆ is > either nonadjacent int )
Def: A Ratio is a comparison of two quantities by division.
Def: A Proportion is an equation that states that two ratios are equal.
Def: Similar Polygons Two polygons such that their corresponding angles are
congruent and the lengths of the corresponding sides are proportional.
P22 Angle-Angle (AA) Similarity Postulate If two angles of one triangle are
congruent to two angles of another triangle, then the two triangles are similar.
(AA Sim or AA  AA)
Following the AA Similarity Postulate, the following two theorems may be used:
Thm (Not in Book): If two triangles are similar, their corresponding sides are in
proportion. (~∆s ↔ corr sides in prop)
Thm (not in Book) Equality of Cross Products: In a proportion, the product of the
means equals the product of the extremes. (prop → prod means = prod extremes)
Th 6-2: Side-Side-Side (SSS) Similarity Theorem If the corresponding side
lengths of two triangles are proportional, then the triangles are similar.
(SSS ~ thm)
Th 6-3: Side-Angle-Side (SAS) Similarity Theorem If an angle of one triangle is
congruent to an angle of a second triangle and the lengths of the sides including these
angles are proportional, then the triangles are similar. (SAS ~ thm)
Th 6-4: Triangle Proportionality Thm If a line parallel to one side of a triangle
intersects the other two sides, then it divides the two sides proportionally.
Th 6-5: Converse of Triangle Proportionality Thm If a line divides two sides
of a triangle proportionally, then it is parallel to the third side.
Th 6-6: If three parallel lines intersect two transversals, then they divide the
transversals proportionally.
Th 6-1: Proportional Perimeters If two polygons (triangles) are similar, then the
ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Thm (Not in Book) Proportional Areas - If two polygons (triangles) are similar,
then the areas are proportional to the ratio of the square of the lengths of a pair
of corresponding sides.
Thm (Not in Book) Proportional Volumes - If two polygons (triangles) are
similar, then the volumes are proportional to the ratio of the cube of the lengths of
a pair of corresponding sides.
Thm (In book as a concept) If two triangles are similar, then the measure of the
corresponding altitudes, angle bisectors and medians are proportional to the
measure of their corresponding sides.
Th 6-7: If a ray bisects an angle of a triangle then it divides the opposite sides
into segments whose lengths are proportional to the lengths of the other two
sides.
Th 7-1: Pythagorean Thm In a right triangle, the square of the length of the
hypotenuse is equal to the sum of the squares of the lengths of the legs.
Th 7.2 Pythagorean Thm Converse If the square of the lenght of the longest
side of a triangle is equal to the sum of the squares of the lengths of the other
two sides, then the triangle is a right triangle.
Th 7-3: If the square of the length of the longest side of a triangle is less than the
sum of the squares of the lengths of the other two sides then the triangle is an
acute triangle. (c2 < a2 + b2 then acute)
Th 7-4: If the square of the length of the longest side of a triangle is greater than
the sum of the squares of the lengths of the other two sides then the triangle is
an obtuse triangle. (c2 > a2 + b2 then obtuse)
Def: The geometric mean or mean proportional for any positive numbers a
x b
 . So x 2 = ab and x = ab .
and b is the positive number x that satisfies
a x
Th 7-5: If the altitude is drawn to the hypotenuse of a right triangle, then the
two triangles formed are similar to the original triangle and to each other.
Th 7-6: Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the
right angle to the hypotenuse divides the hypotenuse into two segments. The length of
the altitude is the geometric mean of the lengths of the two segments. (s.a.a.s rule)
Th 7-7: Geometric Mean (Leg) Theorem In a right triangle, the altitude from the
right angle to the hypotenuse divides the hypotenuse into two segments. The
length of each leg of the right triangle is the geometric mean of the lengths of
hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
(h.l.l.s rule)
Th 7-8: 45º-45º-90º Triangle Theorem In a 45º-45º-90º triangle, the hypotenuse
is times as long as each leg.
Th 7-9: 30º-60º-90º Triangle Thm In a 30º-60º-90º triangle, the hypotenuse is
twice as long as the shorter leg, and the longer leg is times as long as the
shorter leg.
Th 8-1: Polygon Interior Angles Theorem The sum of the measures of the
interior angles of a convex n-gon is (n-2)180º.
Corollary: The sum of the measures of the interior angles of a quadrilateral is
360º.
Th 8-2: Polygon Exterior Angles Thm The sum of the measures of the exterior
angles of a convex polygon, one angle at each vertex is 360º.
Def: A Parallelogram is a quadrilateral with both pairs of opposite sides parallel.
(
↔ 2 pr opp sides )
Th 8-3: If a quadrilateral is a parallelogram, then its opposite sides are congruent.
(
↔ 2 pr opp sides  )
Th 8-4: If a quadrilateral is a parallelogram, then its opposite angles are congruent.
(
↔ 2 pr opp s  )
Th 8-5: If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary. (
→ consec s supp)
Th 8-6: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(
↔ diag bisect each other)
Def: Diagonals are segments that connect any two non-consecutive vertices of a
polygon.
Th 8-7: If both pairs of opposite sides of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.(use shortcut from Th 8-3 also)
Th 8-8: If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.(use shortcut from th 8-4 also)
Th 8-9: If one pair of opposite sides of a quadrilateral are congruent and parallel, then
the quadrilateral is a parallelogram. (1 pr opp sides &  →
)
Th 8-10: If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
Def: A Rhombus is a quadrilateral with 4 congruent sides.
(RH ↔
w/ all sides  )
Rhombus corollary - A quadrilateral is a rhombus if and only if it has four congruent
sides. (RH ↔
w/ all sides  )
Th 8-11: A parallelogram is a rhombus if and only if its diagonals are perpendicular.
(RH ↔
w/  diag)
Th 8-12: A parallelogram is a rhombus if and only if each diagonal bisects a pair of
opposite angles. (RH ↔
w/ diag bisect s )
Thm (not in book) If a parallelogram has consecutive sides congruent, then it
is a rhombus. (RH ↔
w/ 2 consec sides  )
Def: A Rectangle is a quadrilateral with 4 right angles. (RE ↔ all rt s )
Rectangle Corollary - A quadrilateral is a rectangle if and only if it has four right
angles.
Th 8-13: A parallelogram is a rectangle if and only if its diagonals are congruent.
(RE ↔
w/  diag)
Thm (not in book) If a parallelogram has 1 right angle, then it is a rectangle.
(RE ↔
w/ ≥ 1 rt )
Def: A square is a parallelogram with 4 congruent sides and 4 right 's.
Square Corollary - A quadrilateral is a square if and only if it is a rhombus and a
rectangle. (SQ ↔ RE & RH)
Def: A Trapezoid is a quadrilateral with exactly one pair of parallel sides, called bases.
(The nonparallel sides are legs.) (TR ↔ quad w/ only 1 pr opp sides )
Def : An Isosceles Trapezoid is a trapezoid with congruent legs.
(isos TR ↔ TR w/ non
sides  )
Th 8-14: If a trapezoid is isosceles, then both pairs of base angles are congruent.
(isos TR ↔ TR w/ base s  )
Th 8-15: If a trapezoid has a pair of congruent base angles, then it is an
isosceles trapezoid. (use Th 8 – 14 shortcut as well)
Th 8-16: A trapezoid is isosceles if and only if its diagonals are congruent.
(isos TR ↔ TR w/ diag  )
Def: The Midsegment of a trapezoid is a segment that connects the midpoints
of the legs of a trapezoid. (Also known as median.)
Th 8-17: Midsegment Theorem for Trapezoids The midsegment of a trapezoid
is parallel to each base and its length is one half the sum of the lengths of the
bases.
Def: A Kite is a quadrilateral that has two pairs of consecutive congruent sides, but in
which opposite sides are not congruent.
(kite → 2 pr consec sides  & opp sides not  )
Th 8-18: If a quadrilateral is a kite, then its diagonals are perpendicular.
(kite →  diag)
Th 8-19: If a quadrilateral is a kite, then exactly one pair of opposite angles are
congruent.
(kite → only 1 pr opp s  )
P 23: Arc Addition Postulate: The measure of an arc formed by two adjacent
arcs is the sum of the measures of the two arcs.
Thm (Not in Book) In a circle, or in congruent circles all radii are congruent.
(all radii in the same circle are  )
Thm (Not in Book) - In a circle or in congruent circles, congruent central angles intercept
congruent arcs. (In a circle,  arcs ↔  central s )
Converse of Theorem above: In a circle or in congruent circles, congruent arcs
are intercepted by congruent central angles. (use same as above thm)
Th 10-1: In a plane, a line is tangent to a circle if and only if the line is
perpendicular to a radius of the circle at its endpoint on the circle.
SHORTENED: In a circle, or in congruent circles, a radius and a tangent are
perpendicular at the point of tangency.
(line tangent to circle   to radius at pt of tangency)
Th 10.2: Tangent segments from a common external point are congruent.
(2 tangents drawn to circle from same external pt are  )
Th 10.3: In the same circle, or in congruent circles, two minor arcs are
congruent if and only if their corresponding chords are congruent.
(In a circle ,  arcs ↔  chords)
Thm (not in book): In a circle, or in congruent circles, parallel chords intercept
congruent arcs between them. ( lines intercept  arcs)
Converse of above Thm (not in Book): In a circle, or congruent circles,
congruent arcs are intercepted by parallel chords.
Th 10.4: If one chord is a perpendicular bisector of another chord, then the first
chord is a diameter.
Th 10.5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects
the chord and its arc. (A diameter  to a chord bisects the chord and its arcs)
Th 10.6: In the same circle, or in congruent circles, two chords are congruent if
and only if they are equidistant from the center. (In a circle, 2 chords
equidistant from the center are  )
Th 10.7: The measure of an inscribed angle is one half the measure of its
intercepted arc. (In a circle, m(inscribed  ) = ½ m(intercepted arc))
Th 10.8 - If two inscribed angles of a circle intercept the same arc, then the angles
are congruent. (In a circle, 2 inscribed s w/ same arc are  )
Th 10.9 - If a right triangle is inscribed in a circle then the hypotenuse is a
diameter of the circle. Conversely, if one side of an inscribed triangle is a
diameter of the circle, then the triangle is a right triangle and the angle opposite
the diameter is the right angle.
SHORTENED: In a circle, or in congruent circles, an inscribed angle open to a semicircle is a right angle. ( inscribed in a semi circle → rt  )
Th10-10: A quadrilateral can be inscribed in a circle if and only if its
opposite angles are supplementary.
Th 10:11 - If a tangent and a chord intersect at a point on a circle then the
measure of each angle formed is one half the measure of its intercepted arc.
Th 10-12: If two chords intersect inside a circle, then the measure of each angle
is one half the sum of the measures of the arcs intercepted by the angle and the
vertical angle.
Th 10-13: If a tangent and a secant, two tangents, or two secants intersect
outside a circle, then the measure of the angle formed is one half the difference
of the measures of the intercepted arcs.
Th 10.14: If two chords intersect in the interior of a circle, then the product of the
lengths of the segments of one chord is equal to the product of the lengths of the
segments of the other chord.
Th 10.15: If two secant segments share a same endpoint outside the circle, then
the product of the lengths of one secant segment and its external segment
equals the product of the lengths of the other secant segment and its external
segment.
Th 10.16: If a secant segment and a tangent segment share an endpoint outside
a circle, then the product of the lengths of the secant segment and its external
segment equals the square of the lengths of the tangent segment.
Th 11 - 8: The circumference C of a circle is C = πd or C = 2πr where d is the
diameter of the circle and r is the radius of the circle.
Th 11 - 9: The area of a circle is π times the square of the radius.
Th 11-10: The ratio of the area of a sector of a circle to the area of the whole
circle (πr2) is = to the ratio of the measure of the intercepted arc to 360º.