Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Cartesian coordinate system wikipedia , lookup
Multilateration wikipedia , lookup
History of geometry wikipedia , lookup
Euler angles wikipedia , lookup
Technical drawing wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
SSS AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. If Sides are congruent and Angles are congruent 1. AB DE 4. A D 2. BC EF 5. B E 3. AC DF 6. C F then Triangles are congruent ABC DEF SSS AND SAS CONGRUENCE POSTULATES POSTULATE POSTULATE 19 Side - 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 SSS AND SAS CONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for proving two triangles are congruent without using all six pairs of corresponding parts. Using the SSS Congruence Postulate Prove that PQW TSW. SOLUTION Paragraph Proof The marks on the diagram show that PQ TS, PW TW, and QW SW. So by the SSS Congruence Postulate, you know that PQW TSW. SSS AND SAS CONGRUENCE POSTULATES POSTULATE POSTULATE 20 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 Using the SAS Congruence Postulate Prove that AEB DEC. 1 2 3 1 Statements Reasons AE DE, BE CE Given 1 2 AEB DEC 2 Vertical Angles Theorem SAS Congruence Postulate MODELING A REAL-LIFE SITUATION Proving Triangles Congruent You are designing the window shown in the drawing. You want to make DRA congruent to DRG. You design the window so that DR AG and RA RG. ARCHITECTURE Can you conclude that DRA DRG ? D SOLUTION GIVEN PROVE DR AG RA RG DRA A DRG R G Proving Triangles Congruent GIVEN DR AG RA RG DRA PROVE D DRG A Statements R G Reasons Given 1 DR AG 2 DRA and DRG are right angles. If 2 lines are , then they form 4 right angles. 3 DRA 4 RA RG Given 5 DR DR Reflexive Property of Congruence 6 DRA DRG SAS Congruence Postulate DRG Right Angle Congruence Theorem Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that ABC FGH. SOLUTION AC = 3 and FH = 3 AC FH AB = 5 and FG = 5 AB FG Congruent Triangles in a Coordinate Plane Use the distance formula to find lengths BC and GH. d= BC = (x 2 – x1 ) 2 + ( y2 – y1 ) 2 (– 4 – (– 7)) 2 + (5 – 0 ) 2 d= GH = (x 2 – x1 ) 2 + ( y2 – y1 ) 2 (6 – 1) 2 + (5 – 2 ) 2 = 32 + 52 = 52 + 32 = 34 = 34 Congruent Triangles in a Coordinate Plane BC = 34 and GH = 34 BC GH All three pairs of corresponding sides are congruent, ABC FGH by the SSS Congruence Postulate.