1 / 19

Congruent Triangle Methods

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

horace
Download Presentation

Congruent Triangle Methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 D F • 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?

More Related