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4.1 Types of Triangles
• You can classify a triangle by its sides and its
angles.
• There are THREE different classifications for
triangles based on their sides.
• There are FOUR different classifications for
triangles based on their angles.
Triangles By Sides
• EQUILATERAL – 3 congruent sides
• ISOSCELES – at least two sides congruent
• SCALENE – no sides congruent
Triangles by Angles
• EQUIANGULAR – all angles are congruent
• ACUTE – all angles are acute
• RIGHT – one right angle
• OBTUSE – one obtuse angle
Scalene Triangles
• No sides are the same length
Isosceles Triangles
• At least two sides are the same length
Acute Triangles
• Acute triangles have three acute angles
Right Triangles
• Right triangles have one right angle
Obtuse Triangles
• Obtuse triangles have one obtuse angle
Classify this triangle.
Right Scalene
Classify this triangle.
Obtuse Isosceles
Classify this triangle.
Acute Scalene
Classify this triangle.
Acute Isosceles
Classify this triangle.
Obtuse Scalene
Classify this triangle.
Right Isosceles
GUIDED PRACTICE
2.
for Examples 1 and 2
Triangle ABC has the vertices A(0, 0), B(3, 3), and
C(–3, 3). Classify it by its sides. Then determine if
it is a right triangle.
ANSWER
ABC is a right Isosceles triangle.
EXAMPLE 2
Classify a triangle in a coordinate plane
Classify PQO by its sides.
Then determine if the triangle
is a right triangle.
SOLUTION
STEP 1 Use the distance formula to find the side lengths.
OP =
=
( x2 – x1 ) 2 + ( y2 – y1 ) 2
( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 =
OQ =
( x2 – x1 ) 2 + ( y2 – y1 ) 2
=
( 6 – 0 )2 + ( 3 – 0 )2
=
5
2.2
45
6.7
EXAMPLE 2
Classify a triangle in a coordinate plane
PQ =
=
( x2 – x1 ) 2 + ( y2 – y1 ) 2
( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 =
50
7.1
STEP 2 Check for right angles.
2–0
The slope of OP is
= – 2.
–2–0
The slope of OQ is 3 – 0 = 1 .
2
6–0
1
The product of the slopes is – 2
= – 1,
2
so OP
OQ and
ANSWER
Therefore,
POQ is a right angle.
PQO is a right scalene triangle.
4.2 Triangles
Classifying Triangles