Download Name Date ______ Geometry Period ______ Triangle Vocabulary

Name ______________________________
Geometry
Date ___________
Period ___________
Triangle Vocabulary:
Equiangular Equilateral Isosceles Scalene Vertex Angle Base Angle –
#1) Triangle ABC is an isosceles triangle. Angle A is the vertex angle, AB=4x-14 and AC=x+10. Find the
length of the legs.
#2) The perimeter of an Isosceles triangle is 70. Two of its sides are equal and the third side is five less than the
equal sides. Find the length of the three sides.
#3) A scalene triangle has three unequal sides. The first side of a triangle is three times the second side. The third
side is twelve more than the second side. If the perimeter is 57 inches, find the dimensions of the scalene triangle.
1
Name ______________________________
Geometry
Date ___________
Period ___________
Parts of a Triangle:
 Interior angles
 Exterior angles
 Adjacent angles
 Supplementary angles
 Remote interior angles
Theorems and Corollaries:
Angle Sum Theorem: The angles of a triangle add up to a _________.
#1)
#2)
#3)
#4)
2
Name ______________________________
Date ___________
Geometry
Period ___________
Example #5: Find the measure of each numbered angle in the figure if AB || CD .
A
B
5
C
2
60°
135 ° 1
3
4
D
Example #6: Find the measure of each angle.
3
4
1
5
2
6
68°
Exterior Angle Theorem: the measure of an _____________ is = to the sum of the two _______________.
#7)
#8)
3
Name ______________________________
Geometry
Date ___________
Period ___________
#8)
Theorems:
Isosceles Triangle Theorem- If two sides of a triangle are ___________, then the _______________ opposite
those sides are _____________.
Theorem: If two angles of a ___________ are congruent, then the __________ opposite those angles are
____________.
Directions: Find x and y.
Example #1)
Example #2)
M
14y + 29
y
7x - 10
O
65
x
3x + 40
17y - 78
x
P
4
Name ______________________________
Geometry
Example #3)
6x - 6
Date ___________
Period ___________
32°
24
y
30
Example #4) If Angle X is the vertex angle of an isosceles triangle and angle X=52, find angle Y and angle Z.
X
Y
Z
Example #5) In isosceles triangle DEF, Angle D is the vertex angle. If Angle E=2x+40 and angle F=3x+22,
find the measure of each angle of the triangle.
Example #6) In isosceles triangle RST, Angle R is the vertex angle. If Angle S=7x-17 and Angle T=3x+35,
find the measure of each angle of the triangle.
5
Name ______________________________
Geometry
#7)
Date ___________
Period ___________
Congruent Triangles: Two triangles are _________________ if and only if their ____________________
parts are congruent.
Directions: Write a congruence statement.
Example #1)
E
B
F
A
D
C
Example #2)
D
A
C
E
F
B
Example #3: Use the congruence statement to complete the correspondences if RST  ABC.
C  ____
R  ____
AC  ____
ST  ____
RS  ____
6
Name ______________________________
Geometry
Date ___________
Period ___________
Congruency Theorems:
#1) __________: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles
are congruent.
#2) ________: If two sides and the included angle of one triangle are congruent to two sides and an included
angle of another triangle, then the triangles are congruent.
#3) ___________: If two angles and the included side of one triangle are congruent to two angles and the
included side of another triangle, the triangles are congruent.
#4) ____________: If two angles and a non-included side of one triangle are congruent to the corresponding
two angles and side of a second triangle, the two triangles are congruent.
#5) ____________: If the hypotenuse and a leg of a right triangle are congruent to the corresponding
hypotenuse and leg of a second triangle, the two triangles are congruent. (Must be a right triangle to use this
theorem!!!!)
* ____________: This is not a valid theorem because __________________________.
Directions: Determine whether the triangles are congruent, and if so by which theorem.
)
Example #1)
Example #2)
Example #3)
7
Name ______________________________
Geometry
Date ___________
Period ___________
Directions: For each diagram, write a congruence statement. Then list the theorem that is used to show the
triangles are congruent.
Example #1)
Example #2)
D
Z
N
K
F
G
E
X
Y
F
O
L
Example #3)
Example #4)
Z
P
X
O
Y
S
#5)
#6)
8
Name ______________________________
Geometry
Directions: Write a two column proof.
Date ___________
Period ___________
Example #7)
Given:
Z
C
ABC and XYZ are right triangles.
A and X are right angles.
BC  YZ
B  Y
Prove:
A
ABC  XYZ
B
X
Y
Example #8)
C
Given: BD is a perpendicular bisector of Triangle ABC.
Prove:
D
ABD  CBD
A
B
Directions: Mark all congruent parts. Indicate the postulate that can be used to prove their congruence.
Example #4)
T
R
L
RL  ST
ST bi sec ts RSL
S
9
Name ______________________________
Geometry
Example #5)
Date ___________
Period ___________
D
A
AD || GR
AD  GR
G
R
Example #6)
AB  BC
B
AD  CD
A
D
C
Directions: Write a two column proof.
S
Example #7)
Given: 1 and 2 are right
5
angles , ST  TP.
Prove: RTS  RTP
T
1
3
2
4
R
6
P
W
Example #8)
Given: WZ  YZ
VZ  ZX
Prove: VZW  XZY
V
Z
X
Y
10
Name ______________________________
Geometry
Example #9)
Given: BE bi sec ts AD,
A  D
Date ___________
Period ___________
A
C
E
Prove:
1
AB  DC
2
B
D
Example #10)
Given: Q and S are right angles. QR  SR
P
Prove: P  T
Q
R
S
T
11