INCLUDED??????INCLUDED??????� CA & AR

� ∠R & ∠C

� ∠Α IS INCLUDED BETWEEN ____ & ____

� RC IS INCLUDED BETWEEN ____ & _____

C

A

R

GEOM Drill 12/17/14GEOM Drill 12/17/14

How do we know two How do we know two figures are congruent?figures are congruent?

� If all corresponding sides and angles are congruent

Objective:Objective:To determine ways to

prove triangles congruent

POSTULATE - SSS POST.POSTULATE - SSS POST.� If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.

POSTULATE - SAS POST.POSTULATE - SAS POST.

� If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent.

POSTULATE - ASA POST.POSTULATE - ASA POST.� If two angles and the included

side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent.

� To determine if triangles are congruent, what would you have to measure?

� SSS� SAS� ASA� All sides & all angles.

Which postulate, if any, can be used to prove the triangles congruent?

1. 2.

4.

GT Geometry DrillGT Geometry DrillWrite down the name of the figure described. Only 1 figure. I will keep giving hints

Hint 1 : I am a special polygonHint 2: I have three sidesHint 3: I have an angle that is neither obtuse

or acuteHint 4: My sides have a special relationship

Right Triangle

VOCABULARYVOCABULARY

� HYPOTENUSE

� LEGS

� ∠D IS A RIGHT ANGLE

� FE IS CALLED THE ___?_______

� DF & DE ARE CALLED ____?____

F

D

E

Geometry ObjectiveGeometry Objective

� STW continue to prove triangle congruent

Given: AB || DC; DC Given: AB || DC; DC ≅≅ AB ABProve: ABC ∆Prove: ABC ∆ ≅≅ CDA∆ CDA∆

D C

A B

ProofProof

Statement � � AC ≅ AC� < BAC ≅ _______

� ∆ABC ≅ CDA∆

Reason� Given� ____________� If _________

____________

� ____________

Given: RS ST; TU ST; V is the Given: RS ST; TU ST; V is the midpoint of STmidpoint of ST

Prove: RSV ∆Prove: RSV ∆ ≅≅ UTV∆ UTV∆

R S

TU

V

⊥ ⊥

ProofProof

Statement Reason

AAS THEOREM AAS THEOREM If two angles and a non-included

side of one triangle are congruent to two angles and a non-included side of another triangle then the triangles are

congruent.

GT GeometryGT GeometryGiven:

Prove:

A

BC

D

E

F

FEDECBAB ⊥⊥ ; ACFDFEAB ≅≅ ;

FEDABC ∆≅∆

Pythagorean TheoremPythagorean Theorem

a

bc

Pythagorean TheoremPythagorean Theorem

a

bc a2 + b2 = c2

HLTHEOREMHLTHEOREMIf the hypotenuse and a leg of

one right triangle are congruent to the hypotenuse and a leg of another right triangle , then the triangles are congruent.