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NOTES CLASSIFYING TRIANGLES
CLASSIFYING TRIANGLES BY ANGLES
A right triangle
An obtuse triangle
An acute triangle
An equiangular triangle
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In an acute triangle,
CA, k ',
In an obtuse triangle
the angles are
In a right triangle
In an equiangular
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angle is
angle is
triangle, ,_.,i
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Scalene Triangle
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are
CLASSIFYING TRIANGLES BY THEIR SIDES
Isosceles Triangle
Equilateral Triangle
two sides are congruent
At least (7,- sides are
congruent.
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All
congruent
sides are
. The angle formed by
— triangle the two congruent sides are called `ce.c7:::
Z.The other two angles are 10 0.3€..- angles. The side Opposite the
In an
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the legs is the
angles
vertex is the
Triangle ABC is isosceles
A
What is the vertex?
What sides are legs?
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What side is the base?
and Z
What angles are base angles?
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Symbols and Definitions in Geometry
Symbols save time and space when writing. Here are the most common geometrical symbols:
Symbol
Meaning
Example
In Words
A
Triangle
AABC has 3 equal
sides
Triangle ABC has three equal sides
Angle
m--ABC is 45°
The measure of the angle formed by
ABC is 45 degrees.
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Perpendicular
AB-LCD
The line AB is perpendicular to line
CD
II
Parallel
EF II GH
The line EF is parallel to line GH
Degrees
360° makes a full circle
Right Angle (90 0 )
L. is 90°
A right angle is 90 degrees
AB
The line between A and B
AB
Line Segment
Line "AB"
.A1.1
The line that starts at A, goes
through B and continues on
Ray "AB"
Congruent (same
AABC ADEF
Triangle ABC is congruent to
triangle DEF
Similar (same
shape, different
size)
ADEF—AMNO
Triangle DEF is similar to triangle
NINO
Therefore
a=b ." • b=a
a equals b, therefore b equals a
Para11 el
TOICE5
MN is parallel to CD
shape and size)
•
'4,
The infinite line that includes A and
The corresponding
congruent sides are marked
with small straight line
segments called hash marks.
The corresponding
congruent angles are marked
with arcs.
Conament Angles
and Congruent
Line Segments
ZCAB is congruent to/ FDE
ZABC is congruent to ZDEF
ZACB is congruent to /DFE
ZCAB ZFDE
ZABC ZDEF
LACB ZDFE
AB is congruent toDE
AC DF
BC is congruent toEF
AB DE
BC EF
AC is congruent toDF
1. Graph AABC using points A(0, -4), B(0, -9) and C(-2, -5).
2. Classify AABC.
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A
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8.
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a. Determine if AABC is scalene, isosceles,
or equilateral. Explain your reasoning.
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b. Determine if AABC is a right triangle.
Explain your reasoning. If it is not a right
triangle, use a protractor to detei mine
what type of triangle it is.
C
CLASSIFY QUADRILATERALS
DEFINITIONS
Quadrilateral:
Parallelogram:
Rectangle:
Rhombus:
Square:
Trapezoid:
2
.
g..!. _2i
_....1.........
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1
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h
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It is given that ABCD is a parallelogram. Graph / lAB CD on the grids provided. Decide whether it is
a rectangle, rhombus, square or none of the above. Justify your answer using the definitions of the
quadrilaterals. Fill in the answers in the space provided and him in this sheet.
1. Points: A(3, 1), B(3, -3), C(-2, -3), D(-2, 1)
SHAPE:
Justification
2. Points: A(0, 4), B(6, -2), C(0, -2), D(-6, 4)
.. _
SHAPE:
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..., i..._v _„....., , v..
v
.
....
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Justification:
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-..... .... _ .....
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1
....
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1
3
3. Points: A(1, 1),B(3, 5), C(5. 1), D(3, -3)
SHAPE:
_
Justification
4. Points: A(2, 5), B(5, 2), C(2, -1), D(-1, 2)
SHAPE:
Justification:
4