Congruent Triangles
• Congruent triangles have• The parts of congruent triangles that "match"are called
In a congruence statement,x
CPCTC.•-COIYZSPO Incy.pcuklV Oonqvve/)) As ave
Examples: Complete each congruence statement.1. ABCA=AEEC) 2. AMLFeAJKN
A GFE
5. APQRæAXYZ. List three pairs of angles that are congruent.
7. Suppose AABC = AEFG. For each of the
following, name the corresponding part.
a. ZA
b. ZBCA
z
e. ZGEF
3. If AABC
then ZC z Z4. If ACAT = ADOG
then ÄC
6. AABC AJKL. List three pairs of sides that arecongruent.
ÆöjIc
8. Suppose AAEB ADEC. Which angle in ADEC corresponds to ZABE?
'I'viangle Congruen€
Side — Side - Side SSS Con ruence PostulateThree sides of one triangle congruent to
so AABC by SS-.
Side - Angle - Side (SAS)Two sides and the included angle of one triangle ace to two side" and the included of atriangle
So AABC by
An le — Side-An le ASA Con ence PostulateTwo angles and the included side of one triangle are congruent to two angles and the included side of a secondtriangle
So AABC DC by ASA.c D
An le-An le- Side AAS Con ence PostulateTwo angles and a non-included side of one triangle are congruent to two angles and a non-included side of a
second triangle
So AABC z AD-EL by ABS c DF
H otenuse — Le HL Con ence Postulate
In a right triangle, the hypotenuse and one leg is congruent to the hypotenuse and leg of another right triangle
(Must be a right triangle)
c
AABC AD-EL by -LEL-
Ass orSSA
Four Markings YOU con odd It 'hoy oron't ojroody morkod:If they share o side, If ou soo 00
fiOtJ'0jo
eongpvt'h/
Practice
Determine if each pair of triangles is congruent by SSS, SAS, ASA, HL, or AAS and finish thecongruence statement. If none of these methods work based on the information given, write "none"and write X on the statement blank.
SAS
ABJG =
avoc AHOT DVR
ACAT = SHIP —
msnow6
ACLD=
triangles Congruence
Detertnino whether the ttionglos 010 congruent. It thoy aro congruent fill in thecongruence statement and name the reason (SSS, SAS, AAS, ASA, or HI). If they are notcongruent. put on X in the congruence statement and writo not
AABD-ACBD by SAS
4)
by SSS
AKJM=AMLKby SAS
10.
AXYZ X by not
AEMNa X by not
AYZA A by xl_v OR AAS
act)EaAFCIH
X by not
12.
by SSS or SAS
GSE Geometry
14. pce13.
AWXY
18. R
16.
AKLp=AMLP by HL AASANSQ = A by
kHC7by AAS
ALMN=A X by z : 21.
AWXYcon:
2)
foil
23. K 24.
ABCE-=A DC F by
AGHJ ANPM=A X by
GSE Geometry Unit 2 - Quadrilaterals and Congruence
Use the given infomnation to mark the diagram appropriately. Fill in the congruence
statement and name the reason (SSS, SAS, AAS, ASA. or HL).
The
28. Given: CD-AB: c
fDEæAhBb by ARS
29. Given: JNæLM; NK=MK, IV
AJKN LEM by SASK'
30. Given: AC=BD; AD BC c
AABC BAD by SSS
31. Given: SQ and PR bisect each otherS
32. Given: GHbisects LEGF; EG=FG
PP
by SAS