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