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Geometry
NAME: _________________________________________
NOTES: Classifying Triangles
PERIOD: ______
DATE: __________________________
Mr. Uhl
Classifying Triangles & Angle Measures in Triangles
A polygon is a closed figure in a plane made up of segments called sides that intersect only at their
endpoints, called vertices. Some names of familiar polygons are:
The least number of sides a polygon can have is _______, we call this polygon a _____________.
Everything you ever wanted to know about triangles (but were afraid to ask)
How do we name this triangle:
A
Name the sides of this triangle:
Name the vertices of this triangle:
B
C
Name the angles of this triangle:
RELATIONSHIPS BETWEEN SIDES AND ANGLES
The side opposite A is ________.
For sides AC and BC the included angle is __________.
CLASSIFYING TRIANGLES USING ANGLES
Every triangle must have two angles that are __________________.
For this reason, triangles can be named based on the measure of the third angle.
Define and make a simple sketch to identify an:
ACUTE TRIANGLE –
OBTUSE TRIANGLE –
RIGHT TRIANGLE –
EQUIANGULAR TRIANGLE –
CLASSIFYING TRIANGLES USING SIDE LENGTHS
Define the following terms used to classify a triangle using its side lengths:
SCALENE TRIANGLE –
ISOSCELES TRIANGLE –
EQUILATERAL TRIANGLE –
RIGHT TRIANGLES – a closer look…
Right triangles have special side names… two sides are called LEGS,
and the longest side is called the HYPOTENUSE.
Which sides are legs and which is the hypotenuse in RST?
R
Mark the right angle using the appropriate symbol.
The hypotenuse of any right triangle is always opposite
T
S
the _____________________________.
ISOSCELES TRIANGLES – a closer look…
Isosceles triangles also have special side names… two sides are called LEGS,
and the third side is called the BASE.
Which sides appear to be the legs and which appears to be the base in UVW?
V
Mark the congruent sides and angles using the
appropriate symbols.
The two congruent angles are called base angles.
U
The angle opposite the base is called the vertex angle.
In UVW shown, the vertex angle is:
W
Isosceles Triangle Theorems:
Base Angles Theorem – If two sides of a triangle are congruent,
then the angles opposite them are congruent.
A
In the diagram... If AB @ AC , then ______________.
Converse of the
B
Base Angles Theorem – If two angles of a triangle are congruent,
then the sides opposite them are congruent.
In the diagram... If B  C, then ______________.
Explain why it follows from these theorems that:
If a triangle is equilateral, then it is equiangular.
If a triangle is equiangular, then it is equilateral.
ANGLE MEASURES IN TRIANGLES
We should already be familiar with the following result...
THE TRIANGLE SUM THEOREM:
The sum of the measures of the angles in a triangle is _______________.
It follows from this theorem that:
The acute angles of a right triangle are ___________________________________.
C
Name________________________________________
More ANGLE MEASURES IN TRIANGLES
Geometry
Exterior Angle Theorem – the measure of an exterior angle of a triangle is equal to the sum
of the measures of the two remote interior angles.
Name the exterior angles in the figure:
5
2
The remote interior angles for 5 are:
3
4
1
m5 = m______ + m______
6
m4 = m______ + m______
m6 = m______ + m______
Examples:
1) x=___________
2) x=___________
3) x=__________
4) x=_______________
5)