GEOMETRY: TRIANGLES
COMMON MISTAKES
1
10/20/2009
Geometry-Classifying Triangles
How Triangles are
Classified
Types-Triangles are classified by Angles or Sides
By AnglesObtuse Triangles-triangles with one obtuse
angle.
Right Triangles-triangles with only one right
angle.
Acute Triangles-triangles with all 3 angles
acute.
Equiangular Triangles- triangles with 3
congruent angles(all 3 angles have the same
measure.
By SidesScalene Triangles- None of the 3 sides are
congruent( have the same length) to each other.
Isosceles Triangles- Two of the 3 sides are
congruent to each other.
Equilateral Triangles- All 3 sides of the
triangles are congruent to one another.



2
Common Mistakes

Confusing the triangles names-using
the names for triangles based on their
angles with those based on the sides
H
E
R
B


S
I
A M
K
Incorrect: Triangle BHS is right .
Triangle IRA is obtuse.
Triangle MEK is
equiangular.
Correct: Triangle BHS is acute .
Triangle IRA is right.
Triangle MEK is obtuse.
10/20/2009
Geometry-Pythagorean Theorem
How to apply the
Pythagorean Theorem
Pythagorean Theorem
states that in a RIGHT
triangle, the following
lengths have this
property…

152 + 362 =
c2

Written in geometry, it’s
A
AB2 + BC 2 =
AC 2
C
3
Common Mistakes

F
15
C
Forgetting to take the
SQUARE ROOT to find the
final length. (i.e. Find the
value of c: 225 + 1296 =
c2
c
36
Incorrect:
1521 = c
V
Correct:
1521 = c2
1521 = c2
39 = c )
B
10/20/2009
Geometry– Proving Triangles Congruent
Names of theorems that
prove triangles congruent:
SSS, SAS, AND ASA
For TRIANGLES TO BE CONGRUENT, the 3 sides and 3
angles that go with each other (called corresponding parts)
must be congruent, (i.e. have the same measurements), It can
be proven that if the following 3 relationships between
triangles are true, then the triangle ARE congruent and all 6
facts (3 pairs of congruent sides and 3 pairs of congruent
angles) are true.
SSS (Side-Side-Side)
If the 3 corresponding sides of one triangle are congruent to
the 3 corresponding sides of another triangle, then the
triangles are congruent.



SAS (Side-Angle-Side)
If two sides and the included angle (the angle formed by
these two sides) of one triangle are congruent to the
corresponding two sides and included angle of another
triangle, then the triangles are congruent.

ASA (Angle-Side-Angle)
If two angles and the included side (the side between these
two angles) of one triangle are congruent to the
corresponding two angles and included side of another
triangle, then the triangles are congruent.
4
Common Mistakes

Confusing which corresponding part are
congruent which results in picking the wrong
theorem.

Example: State the theorem that
makes these two triangles congruent.
N
8
B


8
15
R
8
W
15
8
A
Incorrect: Triangle BNW is congruent to
triangle FAR by ASA.
Correct: Triangle BNW is congruent to
triangle FAR by SSS!
10/20/2009
F
Geometry-Angles continued
Types formed by
Intersecting lines and
Transversals
When a transversal line intersects two other
lines, parallel or not, names are given to the
angles formed based upon the position(s) in
which they lie.
Corresponding Angles occupy the same
position with respect to the intersecting line and
transversal (i.e. angles 1 and 5; 2 and 6; 3 and 7; 4
and 8 )
Alternate Interior Angles lie in the interior
positions, but on opposite sides of the
transversal. (i.e. angles 4 and 6; 3 and 5)
Alternate Exterior Angles lie in the exterior
positions, also on opposite sides of the
transversal. (i.e. angles 1 and 7; 2 and 8)
Same-Side Interior Angles occupy the
interior positions on the same-side of the
transversal. (i.e. angles 4 and 5; 3 and 6)
Same-Side Exterior Angles also occupy the
exterior positions but on the same-side of the
transversal. (i.e. angles 1 and 8; 2 and 7)





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5
Common Mistakes

Incorrectly naming the angles
formed by a transversal.
1
2
4
a
3
5


6
8
b
7
t
Incorrect: Angles 2 and 6 are same-side
interior angles.
Correct: Angles 2 an 6 are corresponding
angles.
10/20/2009
Geometry-Angles continued
Types defined by their Angle
Measurements
Common Mistakes

Acute Angles are angles whose
measurements are between 0˚ and
90˚ (i.e. Angle A).

Right Angles are angles whose
measurements are 90˚ (i.e. Angle b).

Obtuse Angles are angles whose
measurements are between 90˚ and
180˚ (i.e. Angle C).

Straight Angles are angles
whose measurements are 180˚
(i.e. Angle D). Lines are
examples of straight angles.
6

Mistaking the definitions of angles
based upon their measurements.
A
C
B
D

Incorrect: Angle A is an obtuse angle.

Correct: Angle A is an acute angle.
10/20/2009