4.5 ASA and AAS 2017 ink.notebook. November 08, Page ASA and AAS. Page 158. Page 161. Page 162. Page 160. Page 159
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1 4.5 S and S 2017 ink.notebook Page S and S Page 158 Page 159 Page 160 Page 161 Page 162 1
2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 4.5 S and S fter this lesson, you should be able to successfully use S and S to prove triangles are congruent. Press the tabs to view details. Press the tabs to view details. Lesson Objectives Standards Lesson Notes G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.O.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.O.8 Explain how the criteria for triangle congruence (S, SS, and SSS) follow from the definition of congruence in terms of rigid motions. G.O.10 Prove theorems about triangles. NGLE SIE NGLE (S) ONGRUENE POSTULTE 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. and ngle, B E F 2
3 4.5 S and S 2017 ink.notebook For each diagram, determine which pairs of triangles can be proved congruent by the S Postulate. b) H a) G E F 1. Given: B Ç, ÚB ÚB Prove: ÆB ÆB Statements B Reasons 1. B Ç 2. ÚB ÚB ÚB ÚB B = B ÆB ÆB
4 2. Given: S V and T is the midpoint of SV Prove: RTS UTV R T S V U Statements Reasons NGLE NGLE SIE (S) ONGRUENE THEOREM If two angles and a non included side of one triangle are congruent to two angles and the corresponding non included side of a second triangle, then the two triangles are congruent. If ngle, ngle,, E B F 4
5 4.5 S and S 2017 ink.notebook For each diagram, determine which pairs of triangles can be proved congruent by the S Postulate. c) d) B 3. In the diagram, B. Which sides are congruent? Which additional pair of corresponding parts needs to be congruent for the triangles to be congruent by the S Theorem? B 1 2 5
6 4.5 S and S 2017 ink.notebook an the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use Name the triangle congruence postulate you can use to prove each pair of triangles congruent. Then state the triangle congruence. 7. T M N O P V U B E Q P R Q 6
7 4.5 S and S 2017 ink.notebook Flow hart Proof: 10. Given: F bisects ÚE and ÚBF Prove: ÆBF ÆF 3 4 B 2 1 F bisects ÚE ÚF ÚEF F E F bisects ÚBF ÚBF ÚF F F ÆBF ÆF 11. Given: B Ç EF, B = E, Ú ÚF Prove: ÆB ÆEF Statements Reasons B E F 7
8 4.5 S and S 2017 ink.notebook Term/Postulate bbreviation Included Side ngle-side-ngle Picture The side between two angles. It is in the middle of the angles. Included ngle The angle formed by two sides. It is in the middle of the two sides. Side-Side-Side If 3 sides of 2 è's are, then the 2 è are Side-ngle-Side If 2 sides & the included Ú are in 2 è's, then the 2 è are Picture efinition/explanation Term/Postulate bbreviation efinition/explanation If 2 Ú's and the included side are in 2 è's, then the 2 è are ngle-ngle-side If 2 Ú's and the NON-included side are in 2 è's, then the 2 è are Parts of a Right Triangle Hypotenuse: Side opposite the right Ú Leg Hypotenuse Leg: Sides that form a right Ú Leg HypotenuseLeg ongruence orresponding Parts of ongruent Triangles are ongruent If hypotenuse and a leg of one RIGHT è's, If 2 è are to the other RIGHT then the 2 rt è' s è are are, then the corresponding parts are also 8
9 State if the two triangles are congruent. If they are, state how you know. PRTIE
10 Name the triangle congruence postulate you can use to prove each pair of triangles congruent. Then state the triangle congruence. 7. K 8. Q Name the triangle congruence postulate you can use to prove each pair of triangles congruent. Then state the triangle congruence. 9. T W J M L P S R Y X 10
11 11
12 Page 3 12
13 13
14 14
15 nswers: nswers page 1: 1. S 3. S 5. S 7. SSS, ËKJM ËKLM 9. S, ËXYT ËTWX nswers page 2: nswers page 3 & 4:
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