1. Congruent Triangle Methods

2. Side-Side-Side (SSS) Postulate
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

3. Side-Side-Side (SSS) Postulate
If AN≌LC, NP ≌CK, and AP ≌ LK, then ∆APN ≌ ∆LKC .

4. Using SSS Given: MO≌LK and KM≌OL Prove: ∆KOM ≌ ∆OKL
1. MO≌LK and KM≌OL Given
2. KO≌KO Reflexive
3. ∆KOM ≌ ∆OKL SSS Postulate

5. Side-Angle-Side (SAS) Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

6. Side-Angle-Side (SAS) Postulate
If QR≌XY, RS≌XW, and <QRS≌<YXW, then ∆QRS ≌ ∆YXW

7. Using SAS Given: DF≌EG Prove: ∆DEF ≌ ∆GFE 1. DF≌EG Given
2. EF≌EF Reflexive Property
3. <DFE≌<GEF Alt. Interior Angle Thm
4. ∆DEF ≌ ∆GFE SAS Postulate E G

8. Angle-Side-Angle (ASA)Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

9. Angle-Side-Angle (ASA)Postulate
If <Y≅<B, YA≅BA, and <ZAY≅<CAB, then ∆ZAY≅ ∆CAB.

10. Using ASA Given: <Y≅<B and YA≅BA Prove: ∆ZAY≅ ∆CAB
1. <Y≅<B and YA≅BA Given
2. <ZAY≅<CAB Vertical < Thm
3. ∆ZAY≅ ∆CAB SAS Postulate

11. Angle-Angle-Side (AAS) Postulate
If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the two triangles are congruent.

12. Angle-Angle-Side (AAS) Postulate
If <J≅<L, JH≅LM, and <JKH≅<LKM, then ∆JHK≅∆LMK.

13. Using AAS Given: <J≅<L and JH≅LM Prove: ∆JHK≅∆LMK
1. <J≅<L and JH≅LM Given
2. <JKH≅<LKM Vertical < Thm
3. ∆JHK≅∆LMK AAS Postulate

14. Hypotenuse-Leg (HL) Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

15. Hypotenuse-Leg (HL) Theorem
If AC≅PR and CB≅RQ, then ∆ABC≅∆PQR.

16. Using HL Given: LN≅ON, <LMN and <NMO are right angles
Prove: ∆LNM≅∆ONM
1. LN≅ON Given
2. <LMN and <NMO are right angles Given
3. NM≅NM Reflexive
4. ∆LNM≅∆ONM HL Thm

17. NO TRANSPORTATION!
No AAA
No Donkeys

18. On a Coordinate Plane How do you measure the length of a side?
Distance Formula

19. Are these two triangles congruent?