Sec. 4-2 Δ by SSS and SAS Objective: 1) To prove 2 Δs using the SSS and the SAS Postulate.

Sec. 4-2Δ by SSS and SAS

Objective:1) To prove 2 Δs using the SSS and the SAS Postulate

GEOMETRY - CONGRUENT TRIANGLES


𝐴𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒h𝑎𝑠6𝑝𝑎𝑟𝑡𝑠

+3 𝑎𝑛𝑔𝑙𝑒𝑠3 𝑠𝑖𝑑𝑒𝑠

R

P

QA

B

C

A PB Q

C R

AB PQBC QRCA RP

𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔𝑎𝑛𝑔𝑙𝑒𝑠𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔𝑠𝑖𝑑𝑒𝑠If ABC PQR then find the corresponding parts𝑒𝑥𝑎𝑚𝑝𝑙𝑒

CPCTC Theorem CPCTC Theorem CCP TC

orrespondingartsongruentrianglesongruent

in

are

ΔABC ΔPQR

AB PQBC QRCA RP

B

CAQ

R

P

A PB QC R


• In Sec. 4-1 we learn that if all the sides and all the s are of 2Δs then the Δs are .

• But we don’t need to know all 6 corresponding parts are .

• There are short cuts.

POSTULATE 4-1 (SSS)

POSTULATE Side - Side - Side (SSS) Congruence Postulate

Side MN QR

Side PM SQ

Side NP RS

If

If three sides of one triangle are congruent to three sidesof a second triangle, then the two triangles are congruent.

then MNP QRSS

S

S

GEOMETRY SSS CONGRUENCE POSTULATE

Included – A word used frequently when referring to the s and the sides of a Δ.

• Means – “in the middle of”• What is included between the sides BX and

MX?• X• What side is included between B and M?• BM

B M

X

GEOMETRY

POSTULATE 4-2 (SAS)

POSTULATE Side-Angle-Side (SAS) Congruence Postulate

Side PQ WX

Side QS XY

then PQS WXYAngle Q X

If

If two sides and the included angle of one triangle arecongruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

A

S

S

SAS CONGRUENCE POSTULATE

SAS

S A

S S

S

A


AB

C

D

𝑒𝑥𝑎𝑚𝑝𝑙𝑒1

YES, ABC CDA

A

C



S S

S

S

S

S

SSSYES,

PQR RSP

P

Q

R

S



S

AS

SS

A

SASYES,

PQR SQT

P

Q

R

S

T



S

AS SS

A

NO, SASYES,


𝑒𝑥𝑎𝑚𝑝𝑙𝑒 4

S

A

S

S

S

A

NO,SASYES,

GEOMETRY ASA CONGRUENCE POSTULATE

S

POSTULATE 4-3 (ASA)

POSTULATE Angle - Side - Angle (ASA) Congruence Postulate

Side PN SR

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 two triangles are congruent.

then MNP QRS

S

Angle N R

Angle P S

If A

S

A

GEOMETRY AAS CONGRUENCE POSTULATE

S

S

POSTULATE 4-4 (AAS)

POSTULATE Angle - Angle - Side (AAS) Congruence Postulate

Side PM SQ

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

then MNP QRSAngle N R

Angle P S

If A

AS



A

S

A

A

A

S

ASAYES,

PQR PST

P

Q

R

S

T

A A

S

A

S

A



AASYES,

ABC DCB

C

DB

A



A

A

S

A

S

AAASYES,

ABC CDA

A

B

C

D


𝑒𝑥𝑎𝑚𝑝𝑙𝑒 4

NO,

AASYES,AA

SA

SA

S S SASYES,

A A

ASAYES,

𝑙𝑒𝑔

𝑙𝑒𝑔

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

THE THEOREM

THE HYPOTENUSE LEGTHEOREM

GEOMETRY - CONGRUENT RIGHT TRIANGLES

THE THEOREM

h h

𝑙𝑙



h

h

𝑙𝑙


𝐻𝐿YES,

h

h

𝑙

𝑙

𝐻𝐿YES,



SSS SAS

ASA AAS

HL

CONGRUENCE THEOREMS

Sec. 4-2 Δ by SSS and SAS Objective: 1) To prove 2 Δs using the SSS and the SAS Postulate.

Documents

Transcript of Sec. 4-2 Δ by SSS and SAS Objective: 1) To prove 2 Δs using the SSS and the SAS Postulate.