Download 1) List the sides and angles of ΔDEF that are equal to ΔABC. m∠A

IM 1 Investigation 4.1.1B
Alternate WS #1-8
Name
Triangles with the same angle measures and side lengths are called congruent, and the symbol ≅
is used to show that shapes are congruent by listing the shapes in the same order in which
their sides and angles correspond.
For example the triangles shown below are congruent, which is shown as ΔABC ≅ ΔDEF. Writing
the letters in the correct order is important because when the shapes are turned it may be
difficult to initially tell which sides and angles are equal to each other.
A
F
E
D
B
C
1) List the sides and angles of ΔDEF that are equal to ΔABC.
m ∠A =
m ∠B =
m ∠C =
AB =
AC =
BC =
Triangles with the same angle measures and side lengths that are proportional are called
similar, and the symbol ∼ is used to show that shapes are similar by listing the shapes in the
same order in which their sides and angles correspond.
For example the triangles shown below are similar, which is shown as ΔGHI ∼ ΔJKL.
J
2) Measure all of the angles and sides.
m ∠G =
m ∠H =
m ∠I =
m ∠J =
m ∠K =
m ∠L =
GH =
GI =
HI =
JK =
JL =
KL =
G
I
What is the common ration between the sides of ΔGHI and ΔJKL
H
L
K
3) For each pair of triangles shown below measure enough sides and angles of each triangle to
decide if they are similar, congruent, or neither and explain why. Show all measurements that
you make by labeling the triangles. Show how they are similar or congruent by listing the
names with the appropriate symbol between them. (Example: ΔABC ≅ ΔDEF or ΔGHI ∼ ΔJKL)
a)
A
D
C
T
O
G
R
b)
T
B
C
U
A
c)
B
G
L
Y
O
R
4) Measure and label each of the 3 angles and sides in the triangles below. Measure angles to the
nearest degree and sides to the nearest millimeter. Label the angles in each corner and label
the sides on each edge. Then name each triangle based on its sides and angles.
a)
b)
c)
d)
e)
f)
5) Name each angle as acute, obtuse, or right.
a.
F = 150˚
c.
C = 90˚
Type:
Type:
b.
K = 24˚
Type:
d.
M = 45˚
Type:
Complementary Angles: Algles with a sum of 90˚ so they form a right angle.
Supplementary Angles: Angles with a sum of 180˚ so they form a straight angle.
6) Find the measure of angle x in each problem, without using a protractor:
B
a.
A
x
b.
65
x
D
38
x = _____
x = ______
C
7) Find the measure of the angle:
a)
b)
and
and
are supplementary. If
, what is
are complementary. If
, what is
?
_________
?
_________
8) Given that
, and the fact that the angles of a triangle always add to 180 degrees, give the
values of the angles and sides of each triangle. Beware; the triangles are not drawn to scale.
Y
8 in.
X
T
∠R =
ST =
∠T =
XZ =
∠X =
YZ =
∠Y =
Z
11 in.
S
6 in.
R