A(–3, 1),B(–1, 3),C(1, 3),D(3, 1) mAOC = m BOD = 90° EXAMPLE 4 Identify a rotation Graph ABand CD.Tell whether CDis a rotation of ABabout the origin. If so, give the angle and direction of rotation. This is a 90° clockwise rotation.
A(0, 1),B(1, 3),C(–1, 1),D(–3, 2) mAOC < mBOD EXAMPLE 4 Identify a rotation This is not a rotation.
You can see that AC = DF = 3, so AC DF. S EXAMPLE 5 Verify congruence The vertices of ABCare A(4, 4), B(6, 6), and C(7, 4). The notation (x, y)→ (x + 1, y – 3) describes the translation of ABC to DEF. Show that ABC DEFto verify that the translation is a congruence SOLUTION
S Using the Distance Formula, AB=DE=2 2 so AB DE. So, ABC DEFby the SAS Congruence Postulate. ANSWER Because ABC DEF, the translation is a congruence transformation. EXAMPLE 5 Verify congruence Using the slopes, AB DEand AC DF. If you extend ABand DFto form G, the Corresponding Angles Postulate gives you BAC Gand A GEDF. Then,BACEDFby the Transitive Property of Congruence.
Tell whether PQRis a rotation of STR. If so, give the angle and direction of rotation. Yes, triangle PQRis a 180o counterclockwise rotation of STR. for Examples 4 and 5 GUIDED PRACTICE SOLUTION
Show that PQR STRto verify that the transformation is a congruence transformation. Prove :PQR STR statement Reason PQ ST ByHL PQRSTR. So it is a congruence transformation PR SR for Examples 4 and 5 GUIDED PRACTICE SOLUTION (Given) (Given)