Download Applied Geometry

Geometry
Lesson 4 – 1
Classifying Triangles
Objective:
Identify and classify triangles by angle measures.
Identify and classify triangles by side measures.
Classifications of
Triangles by Angles
Acute Triangle
3 acute angles
Obtuse Triangle
1 obtuse angle
Equiangular Triangle
3 congruent acute angles
Right Triangle
1 right angle
Classify each triangle as acute,
equiangular, obtuse, or right.
Acute
Equiangular
Right
Obtuse
Example
Classify triangle PQR as acute, equiangular,
obtuse, or right. Explain your reasoning.
104
Triangle PQR is obtuse since it has 1 obtuse angle
Of 104 degrees.
Your Turn
Use the diagram to classify triangle PQS
as acute, equiangular, obtuse, or right.
90
Triangle PQS is a right triangle since it has a right
angle.
Classifying Triangles by Sides
Equilateral Triangle
3 congruent sides
Scalene Triangle
No congruent sides
Isosceles Triangle
at least 2 congruent sides
Could an isosceles triangle be
equilateral?
So is an equilateral triangle always
isosceles… or an isosceles triangle
always an equilateral triangle?
Classify the following as
equilateral, isosceles, or scalene.
Isosceles
Equilateral
If point M is the midpoint of JL, classify
triangle JKM as equilateral, isosceles, or
scalene. Explain your reasoning.
Find JM.
M is the midpoint.
JM + ML = JL
JM + JM = 1.5
2(JM) = 1.5
JM = 0.75
0.75
0.75
0.75
Def. Of Midpoint
Triangle JKM is an equilateral triangle with all
sides 0.75 units.
Classify triangle KML as equilateral,
isosceles, or scalene. Explain your
reasoning.
Isosceles since two sides are congruent (0.75).
Find the measures of the sides of
isosceles triangle ABC.
4x + 1 = 5x – 0.5
1 = x – 0.5
Since the figure shows the sides equal
1.5 = x
AC = 4x + 1= 4(1.5) + 1 = 7
BC = 5x – 0.5 = 5(1.5) – 0.5 = 7
AB = 9x – 1 = 9(1.5) – 1 = 12.5
AC = 7
BC = 7
AB = 12.5
Find the measures of the sides of
equilateral triangle FGH.
Since all sides are equal any 2
2y + 5 = 3y – 3
of the 3 sides can be set equal.
5=y–3
8=y
FG
=
FH
=
GH
=
21
FG = 2y + 5 = 2(8) + 5 = 21
FH = 5y – 19 = 5(8) – 19 = 21
GH = 3y – 3 = 3(8) – 3 = 21
Homework
Pg. 238 1 – 14 all, 16 – 44 EOE,
78 – 84 E