Download 5 Triangle Congruence Postulates Powerpoint

The Fast Food Factory
Sandwich Shop
by Mrs. Bentz FMHS
YUM!
Which sandwich is good to eat?
SSS = Spicy Summer
Sausage
 AKA: Side Side Side (SSS)
 3 pairs of Congruent Sides
 By definition of a triangle: If you have
three congruent pairs of sides, you must
have 3 pairs of congruent angles.
#1 SSS

If 3 sides of 1 triangle are congruent to 3
sides of another triangle, then the two
triangles are congruent.
S 1.5in
S 1.5in
2in S
2in S
S
3in
S
3in
Awesome Authentic Anchovy



AKA: Angle Angle Angle (AAA)
3 pairs of congruent angles
Do they have to all be the same size?
#2 AAA
 If 3 angles of 1 triangle are congruent to 3
angles of another triangle, then the
triangles are similar but not necessarily
congruent
A
100°
A
100°
50°
A
50°
30°
A
A
30°
A
Succulent Aromatic
Swine
• AKA: Side Angle Side (SAS)
• The angle is “sandwiched”
between the two sides
Oink
#3 SAS

S
If two sides and the included angle of 1
triangle are congruent to the 2 sides and
included angle of another triangle, then
the two triangles are congruent.
S 2in
2in
50°
A
5 in
S
50°
A
5 in S
Super Sized Antelope
• AKA: Side Side Angle (SSA)
• Watch out! We don’t allow bad words in
Geometry land….
#4 SSA
 Does not prove triangles are congruent
A
A
A
40°
S
40°
2 in
S 2 in
S 2 in
1.5 in
S
1.5 in
S
1.5 in
S
40°
Appetizing Sesame Avocado


AKA: Angle Side Angle (ASA)
The side is “sandwiched” between two angles
#5 ASA

If 2 angles and the included side of 1 triangle
are congruent to the 2 angles and included side
of another triangle, then the 2 triangles are
congruent.
40°
A
40°
70°
A
70°
2.5 in
S
A
2.5 in
S
A
Aunt Annie’s Steak
► AKA:
Angle Angle Side (AAS)
► Not the “sandwiched” side
► Can be either of the two sides
#6 AAS
• If 2 angles and a side of 1
triangle are congruent to 2
angles and a side of another
triangle, then the 2 triangles are
congruent
A
A
A
95°
A
47°
1.8 in S
95°
47°
1.8 in S
Heaping Left-overs
AKA: Hypotenuse Leg
 You must have two right triangles to use
this theorem
 Helps us not say the bad word

#7 HL

In a right triangle, if the hypotenuse and
leg of one triangle are congruent to the
hypotenuse and leg of another triangle,
then the triangles are congruent.
3 in
1.5 in
L
H
3 in H
1.5 in
L