Transcript Triangle Congruency

Triangle
Congruency
Classifying Triangles by Sides
Equilateral
Triangle
Isosceles
Triangle
3 congruent sides
At least 2
congruent sides
Scalene
Triangle
No congruent
sides
Classifying Triangles by Angles
Acute
Triangle
3 acute angles
Equiangular
Triangle
Right
Triangle
Obtuse
Triangle
3 congruent angles
1 right angle
1 obtuse angle
Note: An equiangular triangle is also acute.
Terms to remember
B
Vertex
Plural: Vertices
A
C
Vertex
Vertex
More terms
B
side opposite  C
A
C
adjacent sides
Triangle Sum Theorem
The sum of the measures of the interior angles of a
triangle is 180°.
B
A
C
mA + m B + m C = 180°
Term
congruent figures – Two geometric
figures that have exactly the same size
and shape. All pairs of corresponding
angles and sides are congruent.
symbol: 
Example 1
Identify all pairs of congruent corresponding
parts and write a congruence statement
A  F, C  D, B  E
AB  FE, BC  ED, CA  DF
∆ABC  ∆ FED
M
Example 3
T
(2x+30)°
Find the value of x.
N
55°
65°
L
R
mM = 180º - 55º - 65 º
mM = 60 º
mM = mT
60 = 2x + 30
x = 15
S
Try This!
Find the value of x.
B
87°
A
22°
F
C
(4x+15)°
D
E
Side-Side-Side (SSS)
Congruence Postulate

If three sides of one triangle are congruent to three
sides of a second triangle, then the two triangles
are congruent.
Q
M
If Side
Side
Side
MN  QR,
NP  RS, and
PM  SQ,
S
then MNP  QRS
R
N
P
T
S
Example 1
V
M
I
C
Given: CI  MV, IS  VT, SC  TM
Prove: CSI  MTV
Statements
1. CI  MV, IS  VT, SC  TM
2.
CSI 
MTV
Reasons
1. Given
2. SSS Congruence Post.
Side-Angle-Side (SAS)
Congruence Postulate

If two sides and the included angle of one triangle
are congruent to two sides and the included angle
of a second triangle, then the two triangles are
congruent.
X
If Side
Angle
Side
PQ  WX,
Q  X, and
QS  XY,
then PQS  WXY
Q
P
Y
W
S
C
B
Example 2

1
Prove: ∆AEB  ∆CED
E
2
D
A
Statements
Reasons
1. AE  CE, BE  DE
1. Given
2. 1  2
2. Vertical Angles Theorem
3.
AEB 
CED
3. SAS Congruence Post.
Angle-Side-Angle (ASA) Congruence
Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of a
second triangle, then the two triangles are congruent.
B
E
A
C
D
F
If A  D, AC  DF, and C  F,
then ABC  DEF
Angle-Angle-Side (AAS) Congruence
Theorem

If two angles and a nonincluded side of one triangle are
congruent to two angles and the corresponding
nonincluded side of a second triangle, then the two
triangles are congruent.
B
E
A
C
D
F
If A  D, C  F, and BC  EF,
then ABC  DEF
Hypotenuse-Leg (HL)
Congruence Theorem

If the hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and a leg of a
second right triangle, then the two triangles are
congruent. A
D
B
C
E
If BC  EF and AC  DF, then
F
ABC 
DEF.
Example 2
Is it possible to prove that the triangles are congruent?
If so, state the postulate or theorem you would use.
H
E
Q
N
G
J
F
Yes! AAS
M
P
No!
Try This!
Is it possible to prove that the triangles are congruent?
If so, state the postulate or theorem you would use.
C
E
1
2
4
D
3
Yes! ASA
F
G
No! AAA is NOT a
congruence postulate
or theorem
Homework
Page 238 numbers 1-3, 13,14
 Page 244 numbers 2, 4, 10, 12, 14, 15
 Page 251 Numbers 2-14 Evens
