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Transcript
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 • Given: MO≌LK and KM≌OL • Prove: ∆KOM ≌ ∆OKL 1. MO≌LK and KM≌OL 2. KO≌KO 3. ∆KOM ≌ ∆OKL Given Reflexive SSS Postulate 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. Side-Angle-Side (SAS) Postulate If QR≌XY, RS≌XW, and <QRS≌<YXW, then ∆QRS ≌ ∆YXW Using SAS D • Given: DF≌EG • Prove: ∆DEF ≌ ∆GFE 1. DF≌EG 2. EF≌EF 3. <DFE≌<GEF 4. ∆DEF ≌ ∆GFE E F G Given Reflexive Property Alt. Interior Angle Thm SAS Postulate 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. Angle-Side-Angle (ASA)Postulate • If <Y≅<B, YA≅BA, and <ZAY≅<CAB, then ∆ZAY≅ ∆CAB. Using ASA • Given: <Y≅<B and YA≅BA • Prove: ∆ZAY≅ ∆CAB 1. <Y≅<B and YA≅BA 2. <ZAY≅<CAB 3. ∆ZAY≅ ∆CAB Given Vertical < Thm SAS Postulate 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. Angle-Angle-Side (AAS) Postulate • If <J≅<L, JH≅LM, and <JKH≅<LKM, then ∆JHK≅∆LMK. Using AAS • Given: <J≅<L and JH≅LM • Prove: ∆JHK≅∆LMK 1. <J≅<L and JH≅LM 2. <JKH≅<LKM 3. ∆JHK≅∆LMK Given Vertical < Thm AAS Postulate 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. Hypotenuse-Leg (HL) Theorem • If AC≅PR and CB≅RQ, then ∆ABC≅∆PQR. Using HL • Given: LN≅ON, <LMN and <NMO are • right angles • Prove: ∆LNM≅∆ONM 1. LN≅ON 2. <LMN and <NMO are right angles 3. NM≅NM 4. ∆LNM≅∆ONM Given Given Reflexive HL Thm NO TRANSPORTATION! • No AAA • No Donkeys On a Coordinate Plane • How do you measure the length of a side? • Distance Formula Are these two triangles congruent?
