Download SSS (Side-Side-Side) SAS (Side-Included Angle

Notes T4-66, Triangle Congruence
Congruent Triangles:
____________________________________________________________________________
SSS (Side-Side-Side)
If three sides of one triangle are congruent to three sides of another
triangle, the triangles are congruent.
____________________________________________________________________________
SAS (Side-Included Angle-Side)
If two sides and the included angle of one triangle are congruent to
the corresponding parts of another triangle, the triangles are congruent.
____________________________________________________________________________
ASA (Angle-Included Side-Angle)
If two angles and the included side of one triangle are congruent to
the corresponding parts of another triangle, the triangles are congruent.
____________________________________________________________________________
AAS (Angle-Angle-Side)
If two angles and the non-included side of one triangle are congruent to
the corresponding parts of another triangle, the triangles are congruent.
_____________________________________________________________________________
HL (Hypotenuse-Leg) **for Right Triangles Only**
If the hypotenuse and leg of one right triangle are congruent to the
corresponding parts of another right triangle, the right triangles are congruent.
____________________________________________________________________________
ASS (Angle-Side-Side)
AAA (Angle-Angle-Angle)
Notice these triangles ARE NOT CONGRUENT!!!
Determine which shortcut can be used to prove the following triangles are congruent. Write
the congruence statement and the transformation for each of the following.
1.
2.
A
A
3.
U
B
B
C
X
F
D
D
W
∆ABF
∆UVX
by __________
K
∆ABD
by __________
___________________
4.
C
V
C
by __________
__________________
5.
B
___________________
6.
C
E
R
T
C
T
I
A
R
A
D
A
F
∆IKT
by __________
___________________
∆ABC
by __________
__________________
∆ACT
by __________
___________________
B
Worksheet T4-66, Congruent Triangles
Name: ________________________________ Date: ___________________ Period: _____
Use the markings on the figures and any other valid deductions to determine if the given triangles are
congruent. If yes, complete the congruence statement and give the reason. If not, write “not possible”
and do not complete the statement. Write the transformation above the problem.
1. ∆ ABC  _________
F
by __________
1.
C
C
F
2.
D
__________________
E
2. ∆ ABC  _________
A
B
A
by _________
B D
E
__________________
3. ∆ ABC  _________
by __________
__________________
C
3.
B
4.
C
B
A
4. ∆ ABC  _________
by __________
A
D
A
F
D
__________________
5. ∆ ABC  _________
5.
6.
C
D
by __________
E
.
__________________
6. ∆ ABC  _________
A
B
by __________
__________________
7. ∆ ACD  _________
C
C
7.
D
B
F
A 8.
E
F
B
by __________
___________________
8. ∆ ABC  _________
by __________
A
B
__________________
9. ∆ ABC  _________
C
D
C
D
F
E
D
10.
9.
by __________
__________________
10. ∆ ABD  ________
by __________
A
B D
E
A
B
C
T
11. Given: GHU  TKL
mG = ________
35
G
y = ________
7y
mU = ________
x = ________
GH = ________
H
15
L
4z + 1
E
U
x+5
G
12. Given MAD  GAB
mGAB = ______
K
x–3
3x
x = ________
M
mABG = ______
2x
A
80
B
mAMD = ______
13. Given: TAC  BER
mA = ________
D
x = ________
mC = _______
y = _______
RE = ________
z = _______
R
T
y
24
10
3x
A
14.
Match the vocabulary word with the definition.
___
___
___
___
___
___
___
___
___
___
___
___
a polygon with congruent angles
a polygon with nine sides
a slide transformation
a closed figure made up of line segments
a triangle with congruent base angles
a seven sided polygon
a flip transformation
a line which a figure can fold on to map onto itself
a polygon with congruent sides and angles
a triangle with a hypotenuse
a polygon with eleven sides
a polygon which a rubber band fits around tightly
15.
Complete each statement:
C
B
21
a. concave
b. reflection
c. dodecagon
d. equiangular
e. right triangle
f. dilation
g. nonagon
h. convex
i. polygon
j. translation
l. reflection line
m. equilateral
n. heptagon
o. isosceles triangle
p. regular
q. undecagon
r. scalene triangle
s. pentagon
a. The sum of the 2 shortest sides of a triangle is greater than the _______________.
b. In a right triangle, the ___________________ is the longest side.
c. In an isosceles triangle the base angles are ________________.
d. The sum of the exterior angles in a convex polygon is _____________.
e. The sum of the interior angles in a convex polygon is __________________.