MATH SOLVE

9 months ago

Q:
# If triangles ABC and XYZ are in perspective, name or describe the points that must be collinear according to the Desargues’ theorem.a.AB and XZ, AC and XY, BC and YZc.AB and BC, AC and XZ, BC and YZb.AB and XY, AC and XZ, BC and YZd.AB and XY, AC and XY, BC and YZ

Accepted Solution

A:

Answer:b. AB and XY, AC and XZ, BC and YZ.Step-by-step explanation:Given two triangles ABC and XYZCorresponding side of AB is XY.Corresponding side of BC is YZ.Corresponding side of AC is XZ.Desargues theorem: If two triangles ABC and A'B'C' in a plane .The line AA', BB' and CC' intersect at a single point if and only if the intersection of corresponding sides (AB.A'B') ,(BC,B'C') and ( AC, A'C') lie on a single line.Therefore, in given triangles ABC and XYZ the line AX, BY, CZ intersect at a single point .Then the intersection of corresponding sides (AB,XY), (BC,YZ) and ( AC, XZ) lie on a single line.By Desargues theorem wwe can say Side AB and XY, AC and XZ, BC and YZ are collinear.Hence, option b is correct.