1. TRIANGLES
C.N.Colón
Geometry
St. Barnabas H.S.
Bronx, NY

2. Classifying Triangles
What You'll Learn
You will learn to identify the parts of triangles and to
classify triangles by their parts.
A polygon is a closed figure in a plane that is the union of line segments such that the line segments intersect only at their endpoints and no segments sharing a common endpoint are collinear.
three
In geometry, a triangle is a polygon formed when _____ noncollinear points
are connected by segments. E D F
The vertex of each angle is a vertex of the triangle. Each side is included between two vertices.
Each pair of segments forms an angle of the triangle. The angle is included between the lines.

3. Included Angles C is the included angle of CA and CB
A is the included
angle of AB and AC
B is the included
angle of BA and BC

4. Included Sides
The side of a triangle that falls between two given angles is called the ___________ of the angles.
included side
It is the one side common to both angles. A B C
AC is the included
side of A and C
CB is the included
side of C and B
AB is the included
side of A and B
You can show that two triangles are congruent by using _________ and the
___________ of the triangles.
two angles
included side

5. Classifying Triangles
Triangles are named by the letters at their vertices.
Triangle DEF, written ______, is shown below.
ΔDEF
vertex
The sides are:
EF, FD, and DE. E D F
angle
The vertices are:
D, E, and F.
The angles are:
E, F, and D.
side
You already know that angles can be acute, obtuse, or right.
Triangles can also be classified by their angles.
All triangles have at least two _____ angles.
acute
The third angle is either _____, ______, or _____.
acute
obtuse
right

6. Classifying Triangles
Classified by
Angles
acute
triangle
obtuse
triangle
right
triangle
60°
80°
120°
17°
43°
30°
60°
40°
3rd angle is
_____
3rd angle is
______
3rd angle is
____
acute
obtuse
right

7. Classifying Triangles
Classified by
Sides
scalene
isosceles
equilateral
___
sides
congruent no
__________
sides
congruent
at least two
___
sides
congruent
all

8. Classifying Triangles
The angle formed by
the congruent sides is called the
___________.
vertex angle
The two angles formed by
the base and one of the
congruent sides are called
___________.
The congruent sides
are called legs.
base angles
leg
leg
The side opposite the vertex
angle is called the _____.
base

9. An equiangular triangle is a triangle that has three congruent angles.
Angles of a Triangle
Theorem
An equiangular triangle is a triangle that has three congruent angles.
The measure of each angle of an equiangular triangle is 60. x°
3x = 180
x = 60

10. Right Triangle A
hypotenuse
leg B C
leg

11. The acute angles of a right triangle are complementary.
Angles of a Triangle
Theorem
The acute angles of a right triangle are complementary. x° y°
x + y = 90

12. You will learn to use the Angle Sum Theorem.
Angles of a Triangle
What You'll Learn
You will learn to use the Angle Sum Theorem.
1) On a piece of paper, draw a triangle.
2) Place a dot close to the center (interior) of the triangle.
3) After marking all of the angles, tear the triangle into three pieces.
then rotate them, laying the marked angles next to each other.
Make a conjecture about the sum of the angle measures
of the triangle.

13. The sum of the measures of the angles of a triangle is 180.
Angle Sum
Theorem
The sum of the measures of the angles of a triangle is 180. z° x° y°
x + y + z = 180

14. In Geometric Diagrams You can ASSUME You CANNOT ASSUME
A line segment is a part of a straight line.
The measure of one segment is equal to, less than, or greater than that of another segment
The point where two segments intersect is a point on each segment
A point is a midpoint of a line segment
Points on a line segment are between the endpoints of that segment
Lines are perpendicular or angles are right . Must have a bracket square at angle.
Points on a line are collinear
Triangle is isosceles or equilateral. Must be shown with tick marks.
A ray in the interior of an angle with its endpoint at the vertex separates the angle into two adjacent angles
The measure of an angle is equal to, less than, or greater than that of another angle another .
A given quadrilateral is a parallelogram, rectangle, square rhombus or trapezoid

15. HOMEWORK p. 27 #3-18 (e)