Name _____________________________
Date ___________________
Period _____
Geometry
Notes/WS – Classifying Triangles & Midsegments
A triangle is a polygon with three sides.
CLASSIFYING TRIANGLES BY SIDES
Isosceles
Equilateral Triangle
Triangle
Scalene Triangle
NO congruent
sides
At least TWO
congruent sides
THREE congruent
sides
CLASSIFYING TRIANGLES BY ANGLES
Right
Obtuse
Equiangular
Triangle
Triangle
Triangle
Acute Triangle
THREE acute angles
ONE right
angle
ONE obtuse
angle
Notice that an
equilateral triangle
is also isosceles. An
equiangular triangle
is also acute.
THREE
congruent angles
Midsegment – a segment that connects the midpoints of two sides of a triangle.
A
LM,MN,LN are the midsegments
B
of triangle ABC.
M
L
N
C
Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is ______
to the ___________ and __________ its length.
EX 1: J,K and L are midpoints.
8
JK = ___
JL = ___
JQ = ___
JP = ___
KR = ___
PR = ___
LR = ___
QL = ___
J
K
6
Q
L
18
R
Perimeter of PQR = ___ Perimeter of JKL = ___
QP = ___
I. Classify each triangle as equilateral, isosceles, or scalene. (Not necessarily drawn to scale.)
1.
2.
8
11
3.
10
4.
6
8
7
8
6
4
11
1
2
4
II. Classify each triangle as acute, obtuse, right, or equiangular.
5.
6.
57
84
III.
9.
7.
115
8.
30
60
60
60
30
45
60
35
Classify each triangle. (Draw a picture to help!)
ABC with AB  BC .
10.
DEF with m E  90 .
11.
JKL with JK  KL  LJ .
12.
MNP with MN  NP  PM .
13. QRS with m Q  145 , m R  15 , and m S  20 .
IV.
In #14-16, DE is a midsegment of ABC. Find the value of x in each problem.
14)
15)
7
E
16)
D
D
x
A
B
B
B
x
D
x
E
16
A
C
E
C
A
42
17) In JKL, R,S and T are midpoints where JR  RK , KS  SL , and JT  TL . Complete each
statement.
a) If RS =12, find JL .
b) If ST = 9, find JK .
c) If KL =16, find RT .
d) If KL =16, find KS and SL .
e) If ST =9, find JR and KR .
f) If RS =12, find JT and TL .
C