Transcript Definitions - cloudfront.net

Definitions
Chapter 3 Lesson 1
Ms. Cuervo
Vocabulary
• Parallel Lines-Coplanar lines that do not intersect
• Skew Lines-noncoplanar lines. Neither parallel or
intersecting.
• Parallel Planes-planes that do not intersect
A LINE AND A PLANE ARE PARALLEL IF THEY
DON’T INTERSECT.
Vocabulary
• Transversal-a line that intersects two or more coplanar
lines in different points.
• Alternate Interior Angles-two nonadjacent interior angles
on opposite sides of a transversal
• Same-side Interior Angles-two interior angles on the same
side of a transversal
• Corresponding Angles-two angles in corresponding
positions relative to the two lines.
Theorem 3-1
• If two parallel planes are cut by a third plane,
then the lines of intersection are parallel.
Properties of Parallel Lines
Chapter 3 Lesson 2
Ms. Cuervo
Postulates
• If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
Theorems 3-2
• If two parallel lines are cut by a transversal,
then the alternate interior angles are
congruent.
Theorem 3-3
• If two parallel lines are cut by a transversal,
then the same-side interior angles are
supplementary.
Theorem 3-4
• If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the
other one also.
Proving Lines Parallel
Chapter 3 Lesson 3
Ms. Cuervo
Postulates
• Postulate 10-If two parallel lines are cut by a
transversal, then the corresponding angles
are congruent.
• Postulate 11-If two lines are cut by a
transversal and corresponding angles are
congruent, then the lines are parallel.
Theorem 3-5
• If two lines are cut by a transversal and
alternate interior angles are congruent, then
the lines are parallel.
Theorem 3-6
• If two lines are cut by a transversal and the
same-side interior angles are supplementary,
then the lines are parallel.
Theorem 3-7
• In a plane two lines perpendicular to the same
line are parallel.
Theorem 3-8
Through a point outside a line, there is exactly
one line parallel to the given line.
Theorem 3-9
• Through a point outside a line, there is exactly
one line perpendicular to the given line.
Theorem 3-10
• Two lines parallel to the third line are parallel
to each other.
Angles of a Triangle
Chapter 3 Lesson 4
Ms. Cuervo
Vocabulary
• Triangle-a figure formed by three segments
joining three noncollinear points.
• Vertex-The points when line segments
intersect (plural is vertices).
• Sides-segments of the triangle
Vocabulary
• Scalene Triangle-No sides are congruent
• Isosceles Triangle-At least two sides
congruent
• Equilateral Triangle-All sides congruent
Vocabulary
• Acute Triangle-Three acute angles
• Obtuse Triangle-One obtuse angle
• Right Triangle-One right angle
• Equiangular Triangle-All angles are
congruent.
Vocabulary
• Auxiliary Line-a line (or ray or segment) added
to a diagram to help in a proof.
• Corollary-a statement that can be proved
easily by applying a theorem.
Theorem
• The sum of the measures of the angles of a
triangle is 180.
Corollaries
• Corollary 1-If two angles of one triangle are
congruent to two angles of another triangle,
then the third angles are congruent.
• Corollary 2-Each angle of an equiangular
triangle has the measure of 60.
Corollaries
• Corollary 3-In a triangle, there can be at most
one right angle or obtuse angle.
• Corollary-The acute angles of a right triangle
are complementary.
Theorem 3-12
• The measure of an exterior angle of a triangle
equals the sum of the measures of the two
remote interior angles.
Angles of a Polygon
Chapter 3 Lesson 5
Ms. Cuervo
Vocabulary
• Polygon- “many angles”
• Convex Polygon-a polygon such that no line containing a
side of the polygon contains a point in the interior of the
polygon.
• Diagonal-segments joining two nonconsecutive vertices
• Regular Polygon-a polygon that is both equiangular and
equilateral.
Theorem 3-13
• The sum of the measures of the angles of a
convex polygon with n sides is (n-2)180
• Each individual angle is n-2(180)
n
Theorem 3-14
• The sum of the measures of the exterior
angles of any convex polygon, one angle at
each vertex, is 360.
Inductive Reasoning
Chapter 3 Lesson 6
Ms. Cuervo
Vocabulary
• Inductive Reasoning-reasoning that is widely
used in science and every day life
Example 1
• After picking marigolds for the first time,
Connie began to sneeze. She also began
sneezing the next four times she was near
marigolds. Based on this past experience,
Connie reasons inductively that she is allergic
to marigolds.
Example 2
• Every time Joseph has thrown a high curve ball to
Angel, Angel has gotten hit. Joseph concludes from
his experience that it is not a good idea to pitch high
curve balls to Angel.
• In coming to this conclusion, Joseph has used
inductive reasoning. It may be that Angel just
happened not to be lucky those times, but Joseph is
too bright to feed another high curve to Angel.
Deductive vs. Inductive
• Conclusion based on
accepted statements
(definitions, postulates,
previous theorems,
corollaries, and given
information)
• Conclusion MUST be true if
the hypotheses are true.
• Conclusions are based on
several past observations
• Conclusion is PROBABLY
true, but not necessarily
true.