Answer:
. (In this problem we prove a fact that you demonstrated experimentally in Problem1 of the fourth assignment.) LetABCDbe a quadrilateral. LetM, N, P,andQbe the midpoints of the sides. Prove the area ofMNPQis one half the area ofABCD.4. (See Figure 1.) Give the proof of Theorem 24 for Case (iii). Given:MandNarethe midpoints ofABandAC,MX⊥AB,NX⊥AC, andXis onBC. To prove:Xis on the perpendicular bisector ofBC.XNCMABFigure 1
5. (See Figure 2). Prove Case (ii) of Theorem 28. Given:A0,B0andC0are collinear.To prove:A0BA0CB0CB0AC0AC0B= 1.C'A'B'ABCFigure 26. (See Figure 3.)Given:6A=6B,AD=BE,6ADG=6BEF.To prove:6CFE=6CGD.FGECDBAFigure 37. Suppose that you have a computer program which can perform the following func-tions:
(a) It can draw points, and draw line segments connecting two points.(b) Given a pointOand a line segmentAB, it can construct the circle with centerOand radius equal to the length ofAB.(c) Given a line segmentAB, it can find the midpoint.(d) Given a lineland a pointP(not necessarily lying onl), it can construct theline throughP
Step-by-step explanation:
