Download Geometry Name:

Geometry
Name:
Classifying Triangles, Angles of Triangles, and Isosceles Triangles - Notes
Classifying Triangles
Angles
Measure of
one angle
is 90
Measure of
one angle is
greater than
90
Sides
Measure of
all angles is
less than 90
At least 2
sides are
congruent
No sides are
congruent
3 congruent sides
3 congruent angles
1. Find x and the measure of each side of equilateral triangle JAG if JA= x + 9, AG = 2x,
and JG = 3x – 9.
A
x=
JA =
AG =
JG =
G
J
2. Find x and the measure of the unknown sides of isosceles triangle EFG if EF = 4x, FG =
2x + 6, and EG = 14.
F
x=
EF =
FG =
E
G
Geometry
Name:
Classifying Triangles, Angles of Triangles, and Isosceles Triangles - Notes
Angle Sum Theorem: The sum of the measures of the angles of a triangle is _____.
W
mW  mA  mY  180
A
Y
Find the measures of the following angles.
R
3.
4.
84
1
C 110
54º
79
2
30
3
O
mR  ______
∆CRO is an __________ triangle
m1  ______
m2  ______
m3  ______
Exterior Angle Theorem: the measure of an exterior angle (1) of a triangle is equal to the
sum of the measures of the two remote interior angles (2 & 3).
3
m1  m2  m3
2
1
Find the measures of the following angles.
5.
3
6.
3
2
50º
60º
1
120º 4
5
125º
56º
m3  ______
78º
m1  ______ m2  ______ m3  ______
m4  ______ m5  ______
Geometry
Name:
Classifying Triangles, Angles of Triangles, and Isosceles Triangles - Notes
The acute angles of a right triangle are ________________________.
4.1 Corollary
1
m1  m2  90
2
There can be at most one right or obtuse angle in a triangle.
4.2 Corollary
R
1
40
C
2
110
30
O
Corollary 4.3
Corollary 4.4
A triangle is equilateral if and only if
it is equiangular.
Each angle of an equilateral triangle measures 60º
60º
60º
60º
Is it a Right Triangle?



Put sides into a2 + b2 = c2, with “c” being the hypotenuse or longest side.
Simplify and see if they are equal on both sides.
If they are equal, then it is a right triangle.
Determine if the following side lengths will form a right triangle. Show all work.
7. 5, 12, 13
YES
NO
8. 4, 6, 8
YES
NO
Geometry
Name:
Classifying Triangles, Angles of Triangles, and Isosceles Triangles - Notes
Properties of Isosceles Triangles
The angle formed by the congruent sides is the
_______________ angle.
I
________
________
D
S
The two angles formed by the base and one of the congruent sides are
called the ___________________ angles.
Isosceles Triangle Theorem:
If two sides of a triangle are congruent, then the angles
opposite those sides are congruent.
Inverse:
If two angles of a triangle are congruent, then the sides
opposite those angles are congruent.
If FS  ST
then F  T
S
S
F
T
If F  T
then FS  ST
T
F
9. In an Isosceles Triangle, the __________ are congruent and
the __________ ______________ are congruent.
̅.
∆DIS is an isosceles triangle with ̅̅̅̅
𝐷𝐼 ≅ 𝐼𝑆
10.
11.
12.
13.
14.
I
What is the vertex angle? ____
If DI = 7, then IS = _____
If mD  70 , then mS  _____
If mD  80 , then mI  _____
If mI  100 , then mD  _____ and mS  _____
15. If DI  IS , then _______≅ _______
D
16. If D  S , then _______≅ _______
17. If mD  3x  20 and mS  2x  5
then find x and mD.
x = _____ and mD = _____
S