Download 4.1 – Classifying Triangles

4.1 – Classifying Triangles
Triangles
• A polygon with three sides.
• The corners are called vertices
• A triangle with vertices A, B, and C is
called “triangle ABC” or “ ABC
Classifying Triangles by Sides
Scalene Triangle
No congruent
sides
Isosceles
Triangle
Equilateral
Triangle
3 congruent sides
2 congruent sides
Classifying Triangles by Angles
Acute Triangle
Obtuse Triangle
All acute angles
1 obtuse angle
Right Triangle
Equiangular Triangle
1 right angle
All congruent angles
Example 1:
Classify triangles by sides and angles
a)
b)
c)
7
40°
15°
25
24
70°
70°
120°
Solutions:
a) Scalene, Right
b) Isosceles, Acute
c) Scalene, Obtuse
45°
Example 2:
Classify triangles by sides and angles
Now you try…
a)
b)
5
3
5
5
4
5
c)
110°
Review: The distance formula
To find the distance between two points in the
coordinate plane…
( x2  x1 )  ( y2  y1 )
2
2
EXAMPLE 3
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 3 Classify a triangle in a coordinate plane (continued)
PQ =
=
( x2 – x1 ) 2 + ( y2 – y1 ) 2
( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 =
50
7.1
STEP 2 Check for right angles by checking the slopes.
There is a right angle in the triangle if any of the
slopes are perpendicular.
2–0
The slope of OP is
= – 2.
–2–0
The slope of OQ is 3 – 0 = 1 .
2
6–0
so OP
OQ and
ANSWER
Therefore,
POQ is a right angle.
PQO is a right scalene triangle.
Example 4:
Classify a triangle in the coordinate plane
Now you try…
Classify ΔABC by its sides. Then determine if the triangle
is a right triangle. The vertices are A(0,0), B(3,3) and
C(-3,3).
Step 1: Plot the points
in the coordinate plane.
Example 4: (continued)
Classify a triangle in the coordinate plane
Step 2: Use the distance formula to find the side lengths:
AB =
BC =
CA =
Therefore, ΔABC is a ______________ triangle.
Example 4: (continued)
Classify a triangle in the coordinate plane
Step 3: Check for right angles by checking the slopes.
The slope of
AB
=
The slope of BC =
The slope of CA =
Therefore, ΔABC is a ______________ triangle.