Transcript Congruent Triangles - Lesson 17

p
b
r
q
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Goal 1: How to identify congruent triangles.
Goal 2: How to identify different types of triangles .
Definition of Congruent Triangles
If ABC is congruent to PQR, then there is a correspondence
between their angles and sides such that corresponding angles
are congruent and corresponding sides are congruent. The
notation ABC  PQR indicates the congruence.
b
p
a
c r
q
a  p
b  q
c  r
ab  pq
bc  qr
ca  rp
By Sides
scalene triangle
no congruent
sides
equilateral
triangle
three congruent
sides
isosceles
triangle
at least two
congruent sides
By Angles
obtuse triangle
one obtuse
angle
acute triangle
three acute
angles
right triangle
one right angle
Equiangular
three congruent
angles
Congruence Again
The congruence symbol ““ has a
different meaning than the equal symbol
“=“. In geometry “=“ means “identical to”
or “exactly the same as,” but ““ means
that the measure (a number value) of two
distinct objects of the same class is the
same, or that the measure of the
corresponding parts of the two objects is
the same.
RECALL: Congruent triangles have 3 pairs of  angles
and 3 pairs of  sides.
Do we want to show that all three pairs of
angles are congruent and that all three pairs of
sides are congruent every time?
YES!!!
You can construct congruent triangles with a
minimum amount of information using the
congruent postulates.
Side-Side-Side (SSS) Postulate:
If all three pairs of corresponding sides of two triangles
are equal, the two triangles are congruent.
If you know:
AB = DE
then you know:
and you know:
ABC  DEF
A =  D
BC = EF
B=E
AC = DF
C=F
Side-Side-Side (SSS) Postulate:
AB = DE
ABC  DEF
A =  D
BC = EF
B=E
AC = DF
C=F
Side-Angle-Side (SAS) Postulate:
If two pairs of corresponding sides and the
corresponding contained angles of two triangles are
equal, the two triangles are congruent.
If you know:
AB = DE
then you know:
and you know:
ABC  DEF
A =  D
B=E
AC = DF
AC = DF
C =  F
Side-Angle-Side (SAS) Postulate:
AB = DE
ABC  DEF
A =  D
B=E
AC = DF
AC = DF
C =  F
Angle-Side-Angle (ASA) Postulate:
If two angles and the contained side of one triangle are
equal to two angles and the contained side of another
triangle, the two triangles are congruent.
If you know:
A=D
then you know:
and you know:
ABC  DEF
AC = DF
B=E
C =  F
AB = DE
BC = EF
Angle-Side-Angle (ASA) Postulate:
A=D
ABC  DEF
AC = DF
B=E
C =  F
AB = DE
BC = EF
Right angle - Hypotenuse-Side (RHS) Postulate:
If the hypotenuse and another side of one right triangle
are equal to the hypotenuse and one side of a second
right triangle, the two triangles are congruent.
If you know:
 A =  D = 90o
then you know:
and you know:
ABC  DEF
B =  E
BC = EF
C=F
AC = DF
AB = DE
Right angle - Hypotenuse-Side (RHS) Postulate:
 A =  D = 90o
ABC  DEF
B =  E
BC = EF
C=F
AC = DF
AB = DE
1. REFLEXIVE
Every triangle is congruent to itself.
2. SYMMETRIC
If ABC  PQR, then PQR  ABC
3. TRANSITIVE
If ABC  PQR and PQR  TUV, then ABC  TUV
CLASS WORK
• Check solutions to lesson 16(3)
• Copy notes from Lesson 17
• Do Lesson 17 worksheet