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Kuta Software - Infinite Geometry
Name___________________________________
Isosceles and Equilateral Triangles
Date________________ Period____
Find the value of x.
1)
2)
7
x
x
I
X
3)
A
6
4)
6
4
x 6x
4
5)
x
6)
180
40°
2 7110
18,4
as
x
7)
x
I
75°
8)
108 x igo
su
54°
1
t
x
x
72
9)
75°
so
10)
as
65°
x
see
so
so
28°
76
x
So
80
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-1-
Worksheet by Kuta Software LLC
11)
12)
122x
gg
60
5832
120°
148°
Go
g
of
62
ad
13)
Go
x
14)
8
−1 + x
12
15) m∠2 = x + 94
8
188sso
it
2
2 x − 12
16) m∠2 = 4 x − 2
M
2
a
ax
ng
M
68°
47
68
47°
17) m∠2 = 12 x + 4
18) m∠2 = 13 x + 3
13 37
180
132 3
34
118°
62
A za
28
14 ÉÉ
I2 th
146°
39
satiatu18028
izxtaos.io
12 120
n
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry
Name___________________________________
Isosceles and Equilateral Triangles
Date________________ Period____
Find the value of x.
7
1)
6
2)
7
x
x
6
6
3)
4
4)
6
x
4
70°
5)
x
75°
6)
40°
x
x
72°
7)
75°
30°
8)
x
75°
x
54°
80°
9)
56°
10)
65°
x
28°
x
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-1-
Worksheet by Kuta Software LLC
122°
11)
60°
12)
x
120°
148°
x
9
13)
12
14)
8
−1 + x
12
15) m∠2 = x + 94
−8
16) m∠2 = 4 x − 2
2
2 x − 12
12
2
68°
47°
17) m∠2 = 12 x + 4
10
18) m∠2 = 13 x + 3
11
2
118°
146°
2
Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
5"2"$Equilateral$and$Isosceles$Triangles$–$Homework$
Do
1) Use&the&figure&to&the&right&to&answer&the&following:&&
a. If& Δ AOD&is&isosceles,&with& OA ≅ OD ,&then& ∠ ______ ≅ ∠ ______ ?&
b. If& Δ BOC&is&isosceles,&with& OB ≅ OC ,&then& ∠ ______ ≅ ∠ ______ ?&
c. If& Δ AOD&is&an&isosceles&right&triangle&with&right& ∠ AOD,&then&the&
measure&of& ∠ A&is&_________.&
2) Find&the&values&of&x&and&y.& &
&
a. &&
&
&
b.&&&
&
&
&
&
c.&&&
&
&
&
3) Construct&an&equilateral&triangle&whose&sides&are&1.25&inches&long.&
4) Given&the&two&congruent&angles,&name&two&segments&that&must&
be&congruent.&
a. ∠ 1 ≅ ∠ 2&
b. ∠ 3 ≅ ∠ 4&
c. ∠ 5 ≅ ∠ 6&
d. Is&the&statement&“ MK ≅ NK if&and&only&if& ∠ 3 ≅ ∠ 4”&true&
or&false?&
5) Complete.&
&
&
&
&
6) &&
&
&
&
&
7) In&equiangular& Δ ABC,&AB&=&4x&–&y,&BC&=&2x&+&3y&and&AC&=&7.&Find&the&values&of&x&and&y.&
8) In&equilateral& Δ DEF,&m ∠ D&=&x&+&y,&m ∠ E&=&2x&–&y.&Find&the&values&of&x&and&y.&
9) The&lengths&of&the&sides&of&a&triangle&are&3t,&5tX12,&and&t&+&20.&Find&the&values&of&t&that&make&the&
triangle&isosceles.&
10)&Write&a&two&column&proof:&&
Given: XY ≅ XZ
&&
Prove: ∠3 ≅ ∠5
5"2"Equilateral-and-Isosceles-Triangles-–-Homework-Solutions1)--a.-- ∠A ≅ ∠D --
b.-- ∠OBC ≅ ∠OCB - -
2)--a.--x-=-60°,--y-=-60°-
-
c.--45°-
b.--x-=-20°,--y-=-70°- -
c.--x-=-7,-y-=-4-
3)--4)--a.-- XK ≅ YK --
b.-- MK ≅ KN - -
5)--a.-- ∠ 3-=-40°,-- ∠ 4-=-40°,-- ∠ 5-=-60°6)--a.--90°-
-
c.-- GK ≅ HK - -
d.--True-
b.-- ∠ 3-=-2x°,-- ∠ 4-=-2x°,-- ∠ 5-=-3x°-
b.--90°-
7)--x-=-2-and-y-=-18)--x-=-40-and-y-=-209)--t-=-6,-8-or-1010)-Statements-
Reasons-
XY ≅ XZ -
Given-
∠3 ≅ ∠4 --
Properties-of-Isosceles-triangles-
∠4 ≅ ∠5 -
Vertical-angles-are-congruent-
∠3 ≅ ∠5 -
Transitive-Property-
-
D
Lesson 4.1 • Triangle Sum Conjecture
Name
Period
Date
In Exercises 1–9, determine the angle measures.
1. p ! ______, q ! ______
2. x ! ______, y ! ______
28!
53! x
y
q
p
82!
3. a ! ______, b ! ______
79!
17!
98!
a 50! b
23!
31!
4. r ! ______, s ! ______,
5. x ! ______, y ! ______
6. y ! ______
t ! ______
100 " x
85!
t
s
x
100!
r
30 ! 4x
y
y
7x
31!
7. s ! ______
8. m ! ______
9. m!P ! ______
c
s
b
35!
c
P
a
m
76!
a
10. Find the measure of !QPT.
11. Find the sum of the measures of
the marked angles.
P
T
Q
S
R
12. Use the diagram to explain why
13. Use the diagram to explain why
!A and !B are complementary.
m!A " m!B ! m!C " m!D.
A
B
D
E
C
B
C
24
CHAPTER 4
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to
Discovering Geometry Practice Your Skills
©2008 Key Curriculum Press
DG4PSA_894_04.qxd
11/1/06
1:24 PM
Page 25
Lesson 4.2 • Properties of Isosceles Triangles
Name
Period
Date
In Exercises 1–3, find the angle measures.
1. m!T ! ______
2. m!G ! ______
T
3. x ! ______
A
x
110!
R
58!
I
G
N
In Exercises 4–6, find the measures.
4. m!A ! ______, perimeter
of "ABC ! ______
A
5. The perimeter of "LMO
6. The perimeter of "QRS is
is 536 m. LM ! ______ ,
m!M ! ______
344 cm. m!Q ! ______,
QR ! ______
M
y"
13 cm
a " 7 cm
39!
R
68!
y
Q
210 m
102! B
m
31 c
S
a
x " 30!
L
163 m
x
O
C
7. a. Name the angle(s) congruent to !DAB.
C
B
b. Name the angle(s) congruent to !ADB.
D
A
!! and BC
!? Why?
c. What can you conclude about AD
8. x ! _____, y ! _____
9. PR ! QR and QS ! RS.
10. Use the diagram to explain
If m!RSQ ! 120°, what is
m!QPR?
4y
why "PQR is isosceles.
Q
Q
70!
2x " y
79! # x
P
R
S
T
R
55!
P
S
Discovering Geometry Practice Your Skills
bye
©2008 Key Curriculum Press
CHAPTER 4
e
25