Download Classifying Triangles by Angles and Sides

Classifying Triangles by Angles and Sides
Name: _____________________________
Geometry
LESSON
4-1
Acute Triangle
Right Triangle
—
—
Obtuse Triangle
—
—
—
—
all acute angles
Equiangular Tri.
—
one right angle
60
—
60
60
one obtuse angle
all angles
o
Classify each triangle by its angle measures. Remember, there are 180 in every triangle.
2.
1.
3.
—
—
—
—
—
—
Classify:_____________
—
—
Classify: _________________
Classify:___________________
32
27
19
65
25
62
third angle = _______
third angle = _______
third angle = _______
Classify:_____________
Classify: ______________
Classify:_______________
Use the figure to classify each triangle by its angle measures.
4. DFG
$
—
5. DEG
—
%
6. EFG
'
—
—
&
Classifying Triangles by Sides
Page 2
LESSON
4-1
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
all sides congruent
Step 1
Step 2
Find the value of x.
QR RS
4x 3x 5
x5
at least two sides
congruent
no sides congruent
2
Def. of segs.
Substitution
Simplify.
X
X
Use substitution to find the length of a side.
4x 4(5)
Substitute 5 for x.
20
Simplify.
1
Each side length of QRS is 20.
3
Classify each triangle by its side lengths.
7. EGF is _____________________
$
8. DEF is _____________________
%
9. DFG is _____________________
'
Find the side lengths of each triangle.
_
X
_
X
_
10.
&
11.
X
X
2
x - 7x + 19
Equation: ________________________
x = _______
Side length = _________
X
Equation: ________________________
x = _______ Side lengths = ________, _________
Classifying Triangles
Page 3
LESSON
4-1
Practice A
Match the letter of the figure to the correct vocabulary word in Exercises 1–4.
1. right triangle
A.
B.
C.
D.
2. obtuse triangle
3. acute triangle
4. equiangular triangle
Classify each triangle by its angle measures as acute, equiangular, right, or obtuse.
(Note: Give two classifications on # 7.)
60
5.
6.
45°
7.
30°
45°
60°
14°
136°
60°
a
b
congruent sides.
8. An isosceles triangle has
triangle has three congruent sides.
9. A(n)
triangle has no congruent sides.
10. A(n)
Classify each triangle by its side lengths as equilateral, isosceles, or scalene.
(Note: Give two classifications on #13.)
12.
11.
13.
1
2
2.5
a
Find the side lengths of the triangle.
Equation: _________________________
x+2
!
x = _______
14. AB #
15
AC b
X6
17
15
"
BC 15. The New York City subway is known for its crowded cars. If all the seats
in a car are taken, passengers must stand and steady themselves with
railings or handholds. How many hand straps could have been made
from 99 inches of steel?
21
14 in.
14 in.
5 in.
__________
G.1.A
Classifying Triangles
Page 4
LESSON
4-1
Practice B
$
Classify each triangle by its angle measures.
(Note: Some triangles may belong to more than one class.)
50°
!
100°
"
40°
1. ABD
2. ADC
______________
_______________
3. BCD
#
_______________
'
(
Classify each triangle by its side lengths.
4.
GIJ
5.
______________
3X 0.4
7.
2
HIJ
_______________
6.
)
6.9
GHJ
*
_______________
0
X 0.1
X 1.4
1
Equation: _____________________________
x = _______
PQ = _______ QR = _______ RP = _______
8.
3
2N 3 3–4
4
7N
10N 21–4
5
1
__
ST = _______ TU = _______ US = _______
4
9. Use
Chelsea
works
the kitchentoofdraw
Pizza
Today
job of
is to
a ruler
andin
a compass
a Pro.
triangle
withher
sides
3 cm, 4 cm, and 5 cm.
6 cmof the
cut pizza
smallsegment.
triangles.Then,
She uses
a cutting
machine,
First
drawinto
a 5-cm
set your
compass
to 3 cm and make an arc from one end
5.7 cm
so every
triangle
comesset
outyour
the compass
same. The
shows
an an arc from the other
5-cm
segment.
Finally,
to figure
4 cm and
make
4 cmend of the 5-cm
example. Mark
She has
beenwhere
told tothe
cutarcs
3 pizza
triangles
for every
guest.
segment.
the point
intersect.
Connect
this point
to the ends of the 5-cm segment.
There will be 250 guests. If the pizza comes in
squares with 20-centimeter sides and she doesn’t waste any
pizza, how many squares of pizza will Chelsea have to cut up?
__________
CM
CM
CM
Page 5
= show work!
Choose the best answer.
‹__›
1. Which list shows all the segments on AC
that contain the point B ?
A
B
C
D
_
A
B
C
D
AC
_
AB ,
_
AB ,
_
AB ,
_ _
BC
,
_
AC
,
_
AC ,
BD
_
AD ,
_
AD ,
_ _
BC
, BD
_ _ _
BC , BD , CD
2. M is between R and S. If RM 21,
RS 15x 3, and MS 9x 12.
Equation: ____________________________
_
3. K is the midpoint of VW . If KV 3x and
KW 5x 10.
6. Two vertical angles are also
complementary. What is the measure
of one of the two vertical angles?
F 90
H 45
G 50
J 25
7. The area of a square is 16 square units.
What is the perimeter?
A 4 units
C 16 units
B 8 units
D 32 units
8. The midpoint of a segment is (8, 5). If
Draw and
label
diagram.
one endpoint
is (0,
1),awhat
is the other
endpoint?
F (16, 9)
H (4, 2)
G (8, 3)
J (4, 3)
x = _______ RS = _______ MS = _______
9. To the nearest tenth, what is the distance
Draw
andand
label(3,
a diagram.
between (7,
4)
1)?
A 5
C 20.5
B 10.4
D 54.5
Equation: ____________________________ 10.x =Which
_______
KV = _______
KW = _______
coordinate
pair represents
the
image of (9, 10) reflected over the
4. Which appears to be an obtuse angle?
x-axis?
2
F (9, 10)
H (9, 10)
4
J (10, 9)
G (9, 10)
3
11. What is the next figure in the pattern?
1
F PQR
G PSQ
0
H R
J P
A
C
B
D
5. Which two angles are supplementary to RLK?
12. For which statement is the converse
false?
1
F If Mary can swim, then she can swim
0
2
the crawl.
,
G If it is raining outside, then the
+
temperature is above freezing.
H If Greg has two children, then he has
one son and one daughter.
__________ and
__________
J If Carolyn can stand up, then she
can walk.