GEOMETRY CONGRUENT TRIANGLES Sec 4 2 by SSS

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

- CONGRUENT TRIANGLES GEOMETRY CPCTC Theorem CPCTC orresponding arts in ongruent riangles are ongruent If ABC PQR then find the corresponding parts P AB PQ B BC QR CA RP A C R Q A P B Q C R

- CONGRUENT TRIANGLES GEOMETRY ΔABC ΔPQR P B A AB PQ BC QR CA RP C R A P B Q C R Q

• 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.

GEOMETRY SSS CONGRUENCE POSTULATE 4 -1 (SSS) POSTULATE Side - Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side S MN QR Side S NP RS Side S PM SQ then MNP QRS

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? X • BM B M

GEOMETRY SAS CONGRUENCE POSTULATE 4 -2 (SAS) POSTULATE Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If Side S Angle A Side S PQ WX Q X QS XY then PQS WXY

- CONGRUENT TRIANGLES GEOMETRY A S D S A C YES, SAS ABC CDA S B

- CONGRUENT TRIANGLES GEOMETRY Q S S S P R S S YES, SSS PQR RSP

- CONGRUENT TRIANGLES GEOMETRY P R S S YES, SAS A Q A S S S T PQR SQT

- CONGRUENT TRIANGLES GEOMETRY S S A S NO, SAS YES,

- CONGRUENT TRIANGLES GEOMETRY S S YES, NO, SAS A A S S

GEOMETRY ASA CONGRUENCE POSTULATE 4 -3 (ASA) POSTULATE Angle - Side - Angle (ASA) Congruence Postulate 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. If A Angle N R Side PN SR S S AAngle P S then MNP QRS

GEOMETRY AAS CONGRUENCE POSTULATE 4 -4 (AAS) POSTULATE Angle - Side (AAS) Congruence Postulate 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. If A Angle N A S Angle P SSide PM SQ R S then MNP QRS

- CONGRUENT TRIANGLES GEOMETRY Q R A S YES, ASA A P A S PQR PST T

- CONGRUENT TRIANGLES GEOMETRY B A S A A A D S A C YES, AAS ABC DCB

- CONGRUENT TRIANGLES GEOMETRY B A A A S S A C YES, AAS A D ABC CDA

- CONGRUENT TRIANGLES GEOMETRY A S A NO, S A A S YES, AAS YES, SAS ASA

GEOMETRY - CONGRUENT RIGHT TRIANGLES

- CONGRUENT RIGHT TRIANGLES GEOMETRY

- CONGRUENT RIGHT TRIANGLES GEOMETRY YES,

- CONGRUENT RIGHT TRIANGLES GEOMETRY YES,

GEOMETRY - CONGRUENT RIGHT TRIANGLES

C O N G R U E N C E T H E O R E M S SAS SSS AAS ASA HL