4.2B and 4.3 Notes

Congruent Triangles and SSS

Definition of Congruent Triangles:If 3 sides and 3 angles of a triangle are equal, then the triangles are congruent

If ∆BDF ∆KCA, then

Corresponding sides are: Corresponding angles are: KCBD

CADF

KABF

B KD CF A

1. Given GEO FUN, name all corresponding angles and sides.

Sides AnglesFUGE

UNEO

FNGO

G FE UO N

2. In the diagram, EFG OPQ. Complete the statement.

7km110°

OP

F

Q

110°

7km

QPO

Side-Side-Side (SSS) Congruence Postulate

A B C D4cm 4cm

E F

CDAB

CFAE

DFBE

If 3 sides of one triangle are _____________ to three sides of a second triangle, then the two triangles are ________________.

congruent

congruent

Decide whether the congruence statement is true. Explain your reasoning.

Yes, SSS

IJH KJH

Decide whether the congruence statement is true. Explain your reasoning.

Yes, SSS

Decide whether the congruence statement is true. Explain your reasoning.

No, AC BD

4. Given:

Prove: ∆ABC ∆ADC

ADAB DCBC

ADAB Given

DCBC Given

ACAC Reflexive Prop.

∆ABC ∆ADC SSS

1. 1.

2. 2.3. 3.

4. 4.

Statements Reasons

AB CB Given

ACD ofmidpoint theis Given

DCAD Def. of Midpt

∆ABD ∆CBD SSS

DBDB Reflexive Prop.

A D C

B

1. 1.

2. 2.3. 3.

4. 4.

5. 5.

Statements Reasons

, is the midpoint of AB CB D AC5. Given: Prove: ∆ABD ∆CBD

bisects , AC DB AD AB6. Given: Prove: ∆ACD ∆ACB

A

BCD

Given

Def. of Segment BisectorDC CBGiven

∆ACD ∆ACB SSS

AC AC Reflexive Prop.

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

Statements Reasons

bisects AC DB

AD AB