9 Dato il triangolo isoscele ABC di base AB, se consideriamo su CA e su CB rispettivamente i due segmenti CD e CE, tali che CD CE, e se il punto F è l intersezione dei segmenti BD e AE, allora il triangolo ABF è isoscele. 91 ESERCIZI Teoremi sulla congruenza s e, sui suoi lati, i segSi considerano l angolo rO menti: OA s, OB r, OC r, OD s tali che OA OC e OB OD. Si ha: a. AD BC; b. AE CE, essendo E il punto di intersezione dei segmenti AB e CD; s. c. la semiretta OE è la bisettrice dell angolo rO 92 PRACTICE WITH CLIL Three non-collinear points In other units, you learnt about what is the midpoint of a segment and how to draw it with a ruler and a compass. However, how would it be if you have the midpoints but not the segment? Starting from non-collinear points P, Q, R, is it possible to draw a triangle ABC which has P, Q, R as midpoints of its sides? You would proceed as follows. Following Theorem 1, you will have points A p q, B q r, C p r. r C q A P P R p R Q Q The definition of triangle would help you drawing the triangle PQR. P B Having A, B, C, the definition of triangle would help you drawing the requested ABC triangle. R A Q Then you draw the straight lines p, q, r which pass through the triangle s vertices and are parallel to the respective opposite sides. This can be done by following the fifth axiom (the parallel postulate). r q P C R Q B P R p Q 471