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February 14, 2015
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Unit 8: Triangle Geometry
Pages
Title
Vocabulary
Classifying Triangles
Transversals
Proof Structure
Basic Triangle Proofs
Congruent Triangles
Congruent Triangles Proofs
Vocabulary
Reflexive Property: a segment
or angle is congruent to itself.
Congruent : two angles,
segments, or figures are
congruent if their measures are
equal.
Midpoint: results in two
segments being congruent.
Segment Bisector: a line that
intersects a segment and cuts it
into two congruent parts.
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Vocabulary
Perpendicular Bisector: a line
that intersects a segment and
cuts it into two congruent parts
and two right angles.
Angle Bisector: a line (or part of
a line) that divides an angle into
two congruent parts.
Vertical Angles: a pair of
congruent opposite angles
formed by two intersecting lines.
Vocabulary
3rd Angle Theorem: If 2 angles of
a triangle are congruent to two
angles of another triangle, then the
3rd angles are also congruent.
Median: a segment that goes from
a vertex to the midpoint of the
opposite side.
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Vocabulary
Altitude: a segment that goes
from the vertex to the opposite
side of a triangle and is
perpendicular to the other side.
Midsegment: a segment which
connects the midpoints of two
sides of a triangle.
Properties
-parallel to the side of the triangle
it does not intersect.
-it is half the length of that same
side.
Vocabulary
Substitution Postulate: if two
things are congruent to the same
thing then they are congruent to
each other.
Addition Postulate: if you add the
same thing to two equal things
then the result is equal.
Subtraction Postulate: if you
subtract the same thing from two
equal things then the result is
equal.
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Classifying Triangles
By Sides:
Scalene Triangle: no
congruent sides.
Isosceles Triangle: two sides
and angles are congruent.
Equilateral Triangle: three
congruent sides and angles.
(Equiangular)
Classifying Triangles
By Angles:
Acute Triangle: all angles
measurements less than 90o.
Obtuse Triangle: one angle
greater than 90o.
Right Triangle: a 90 angleo.
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Quadrilaterals
Parallelogram: Quadrilateral with two pairs of parallel sides.
Rectangle: Quadrilateral where all four angles are right angles.
Square: Quadrilateral where all four sides are of equal length, and
all four angles are right angles.
Rhombus: Quadrilateral where all four sides are of equal length.
Kite: Quadrilateral where two pairs of adjacent sides are of equal
length.
Trapezoid: Quadrilateral where at least one pair of opposite sides
are parallel.
Square: Quadrilateral where all four sides are of equal length, and
all four angles are right angles.
Properties
-The diagonals of the shape
are congruent.
-The diagonals of the shape
bisect each other at right
angles.
-Two pairs of parallel sides.
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Rectangle: Quadrilateral where all four angles are right angles.
Properties
-The diagonals bisect each
other.
-Opposite sides are congruent.
Parallelogram: Quadrilateral with two pairs of parallel sides.
Properties
-Diagonals are not always
congruent.
-Opposite sides are parallel.
-Opposite angles are
congruent
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Rhombus: Quadrilateral where all four sides are of equal length.
Properties
-The diagonals bisect each
other.
-Opposite sides are parallel.
-Opposite angles are
congruent.
Kite: Quadrilateral where two pairs of adjacent sides are of
equal length.
Properties
-One diagonal is bisected.
-Diagonals intersect at right
angles.
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Trapezoid: Quadrilateral where at least one pair of opposite sides
are parallel.
Isosceles Trapezoid
-legs are congruent
-diagonals are congruent
-common base angles are
congruent.
Transversals
Transversal: a line that intersects two or more coplanar lines at
different points.
11-20
Pg
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Transversals
1
3
5
7
2
11-20
Pg
4
6
8
Corresponding Angles: , angles that occupy the same position
relative to the transversal and the two lines.
Alternate Interior Angles: angles that are inside of the two lines
and on opposite sides of the transversal.
Transversals
1
3
5
7
2
4
6
8
Alternate Exterior Angles: angles that are outside of the two
lines and on opposite sides of the transversal.
Same Side Interior Angles: angles that lie between the two
lines and on the same side of the transversal.
Same Side Exterior Angles: angles that lie outside of the two
lines and on the same side of the transversal.
11-20
Pg
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11-20
Pg
Transversals
Ex 1:
140o
Ex 2:
40o
120o
11-20
Pg
Transversals
Ex 3:
2x + 20
x + 10
3x+15
8x-20
February 14, 2015