Download Congruent Triangles - Lesson 17(2)

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-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
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
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
In the diagram below, PA = PB and AC = BC. Explain
why
a)
PAC  PBC
b)  APC =  BPC
SOLUTION:
IN
PACandPBC
, PA = PB
AC = BC
PC = PC
Therefore
PAC  PBC
(SSS)
b) Since the triangles are congruent, then
 APC =  BPC
In the diagram below, AB = AD and BC = DC. Explain
why
 ABC =  ADC
a) ABC  ADC
b)
In the diagram below, AB = AD and BC = DC. Explain
why
 ABC =  ADC
a) ABC  ADC
b)
SOLUTION:
IN
ABCandADC
, AB = AD
BC = DC
AC = AC
Therefore
ABC  ADC
(SSS)
b) Since the triangles are congruent, then
 ABC =  ADC
In the diagram below, E is the midpoint of both AC
and BD. Explain why AB = CD.
By the Opposite Angle Theorem,
 AEB =  CED
SOLUTION:
IN
ABEandCDE
, AE = CE
 AEB =  CED
BE = DE
Therefore
(SAS)
ABE  CDE
b) Since the triangles are congruent, then
AB = CD
In the diagram below, C is the midpoint of both KY
and ZJ. Explain why KZ = YJ.
In the diagram below, C is the midpoint of both KY
and ZJ. Explain why KZ = YJ.
By the Opposite Angle Theorem,
 KCZ =  YCJ
SOLUTION:
IN
KZCandYJC
, KC = YC
 KCZ =  YCJ
ZC = JC
Therefore
(SAS)
KZC  YJC
b) Since the triangles are congruent, then
KZ = YJ
In the diagram below, BC = ED,  OBA =  OEF, and
 OCB =  ODE. Explain why  BOC =  EOD.
By the Supplementary Angle Theorem,
 OBC =  OED
SOLUTION:
IN
OBCandOED ,  OBC =  OED
BC = ED
 OCB =  ODE
Therefore
OBC  OED
(ASA)
b) Since the triangles are congruent, then
 OBC =  EOD
In the diagram below, KF = ST,  ZKG =  ZTU, and 
ZFK =  ZST. Explain why  KZF =  TZS.
In the diagram below, KF = ST,  ZKG =  ZTU, and 
ZFK =  ZST. Explain why  KZF =  TZS.
By the Supplementary Angle Theorem,
 ZKF =  ZST
SOLUTION:
IN
ZKFandZTS ,  ZKF =  ZTS
KF = TS
 ZFK =  ZST
Therefore
ZKF  ZTS
(ASA)
b) Since the triangles are congruent, then
 KZF =  TZS
CLASS WORK
• Check solutions to Lesson 17
• Copy examples from this lesson
• Do Lesson 17(2) worksheet.