Transcript Proving Triangles Congruent

MARK PAUL DE GUZMAN
SSS POSTULATE
SAS POSTULATE
ASA POSTULATE
AAS THEOREM
POSTULATE:
Are accepted as true
statement and are used
to justify conclusions.
THEOREM
Statements that must be
proven true by citing
undefined terms,
definitions postulate and
previously proven
theorems.
SSS POSTULATE:
XY PR
YZ
Y
RQ and
XZ
PQ
P
Q
X
R
Z
Thus, by SSS Postulate,
XYZ
PRQ
If three sides of
one triangle are
congruent to
three sides of
another
triangle, then
the two
triangles are
congruent
SIDE
ANGLE SIDE
SAS POSTULATE:
POSTULATE If two sides and the
GIVEN: BX
TP; <B
< T; BO
A
P
B
T
X
O
CONCLUSION:
BOX
By; SAS POSTULATE
TA
TAP
included angle of
one triangle are
congruent to two
sides and the
included angle of
another triangle,
then the two
triangles are
congruent.
ASA POSTULATE:
GIVEN:
<P
R
<I ;PA
IT;<A
F
T
A
P
CONCLUSION:
RAP
I
FIT
By; ASA POSTULATE
<T
If two angles and
the included side
of one triangle are
congruent to two
angles and the
included side of
another triangle,
then two triangles
are congruent.
AAS Theorem
If two angles and the
non-included side of one
triangle are congruent,
respectively, to the
corresponding angles
and non-included side of
another triangle, then
the two triangles are
congruent.
GIVEN: <A
PROVE:
<D ; <B
ABC
<E ; BC
DEF
STATEMENTS:
1. <A
<D; <B
EF
B
A
D
C
REASONS:
<E; BC
EF
E
F
1. GIVEN
2. m<A = m<D; m<B = m<E
3. m<A + m<B + m<C = 180
m<D + m<E + m<F = 180
4. m<A + m<B + m<C =
m<D + m<E + m<F
5. m<A + m<B+ m<C =
m<A + m<B + m<F
6. m<C = m<F
7. <C
<F
8. BC
EF
2. DEF. OF
ANGLES
3. The Sum of the measures of
the interior angles IS 180.
4. TPE
9. ∆ABC
9. ASA Postulate
∆DEF
5. Substitution
6. APE
7. DEF. OF
8. GIVEN
ANGLES
B
EXAMPLE 1:
GIVEN:
ABC is an isosceles
angle bisector BD
;cut by
PROVE:
A
ABD
BDC
STATEMENTS:
1. BD
2. <C
4.
REASONS:
BD
1. Reflexive Property
<A
3. <ADB
ABD
D
2. Base <‘s of an isosceles
are congruent
<DBC
BDC
3. Definition of angle bisector
4. AAS THEOREM
C
EXAMPLE # 2:
GIVEN: KJ II NM ; KJ
<KJL
<MNL
PROVE:
KJL
STATEMENTS
1. KJ
NM
K
NM
NML
L
N
J
REASONS
M
1. GIVEN
2. < KLJ
< MLN
2. Vertical Angles are Congruent
3. <KJL
<MNL
3.GIVEN
4.
KJL
NML
4. AAS THEOREM