Warm Up 11.09.11Week 4

Describe what each acronym means:

1) AAA 2) AAS

3) SSA 4) ASA

Geometry

4.4 Day 1

I will prove that triangles are congruent using the ASA and AAS Postulates.

ASA - Angle Side Angle Congruence

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

Postulate 21

∆ABC ≅ ∆DEF because of ASA.

∠A ≅ D ∠

∠C ≅ F ∠

≅

CA

B

FD

E

AAS - Angle Angle Side CongruenceIf two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two

triangles are congruent.

Theorem 4.5

∆ABC ≅ ∆DEF because of AAS.

CA

B

FD

E

∠A ≅ D ∠

∠C ≅ F ∠

≅If , and ,

then

Statement Reason

   

   

   

   

   

Ex 1

CA

B

FD

E

∠A ≅ D ∠

Given

∠C ≅ F ∠

Given

Given

∠B ≅ E ∠

Third Angle Theorem (4.3)

Prove Theorem 4.5: ∆ABC ≅ ∆DEF:

∆ABC ≅ ∆DEF ASA ( P21 )

≅

is given.

is given

because of AAS.

∠E ≅ ∠J

∆EFG ≅ ∆JHG

Ex 2 Prove ∆EFG ≅ ∆JHG:

E

F

G

H

J

≅

are vertical angles.∠EGF ≅ ∠JGH

Ex 3 Prove ∆ABD ≅ ∆EBC:C

B

A

DE

Statement Reason

   

   

   

   

   

≅ Given

∥ Given

∠D ≅ ∠C

Alternate Interior Angles Theorem (3.8)

∠ABD ≅ ∠EBC Vertical Angles Theorem (2.6)

∆ABD ≅ ∆EBC ASA

Do: 1

Assignment:

Textbook Page 223, 8 - 22 all.

Is ∆NQM ≅ ∆PMQ? Give congruency statements to prove it.

N Q

PM