MathDB

similar triangles on parallel planes , parallelepiped 1999 Romania NMO VIII p3

Source:

August 14, 2024

geometrysimilar triangles3D geometryparallelepiped

Problem Statement

Let

ABCDA'B'C'D'

be a right parallelepiped,

E

and

F

the projections of

A

on the lines

A'D

A'C

, respectively, and

P, Q

the projections of

B'

on the lines

A'C'

and

A'C

Prove that
a) the planes

(AEF)

and

(B'PQ)

are parallel
b) the triangles

AEF

and

B'PQ

are similar.