c Find two segments in your diagram that must have the same length as BG d How

C find two segments in your diagram that must have

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(c)Find two segments in your diagram thatmusthave the same length asBG.(d)How do the lengths of segmentsBGandGNcompare?August 201937Phillips Exeter Academy
Mathematics 2423.The diagram at right shows three congruent regularpentagons that share a common vertexP. The three poly-gons do not quite surroundP. Find the size of the uncoveredacute angle atP.424.(Continuation) If the shaded pentagon were removed,it could be replaced by a regularn-sided polygon that wouldexactly fill the remaining space.Find the value ofnthatmakes the three polygons fit perfectly.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................P425.You are given a squareABCD, and midpointsMandNare marked onBCandCD,respectively. DrawAMandBN, which meet atQ. Find the size of angleAQB.426.MarkYinside regular pentagonPQRST, so thatPQYis equilateral. IsRY Tstraight?Explain.427.An airplane that took off from its airport at noon (t= 0 hrs) moved according to theformula (x, y, z) = (15,-20,0) +t[450,-600,20]. What is the meaning of the coordinate 0in the equation? After twelve minutes, the airplane flew over Bethlehem, NH. Where is theairport in relation to Bethlehem, and how high (in km) was the airplane above the town?428.Suppose that triangleABChas a right angle atB, thatBFis the altitude drawn fromBtoAC, and thatBNis the median drawn fromBtoAC. Find anglesANBandNBF,given that(a)angleCis 42 degrees;(b)angleCis 48 degrees.429.Draw a parallelogramABCD, then attach equilateral trianglesCDPandBCQto theoutside of the figure. Decide whether or not triangleAPQis equilateral. Explain.430.Suppose thatABCDis a rhombus and that the bisector of angleBDCmeets sideBCatF. Prove that angleDFCis three times the size of angleFDC.431.The midpoints of the sides of a triangle are (3,-1), (4,3), and (0,5). Find coordinatesfor the vertices of the triangle.432.In the diagram at right, a rectangular sheet of paperABCDhas been creased so that cornerAis now placed onedgeCD, atA0. Find the size of angleDEA0, given that thesize of angleABEis(a)30 degrees;(b)27 degrees;(c)ndegrees.433.Suppose that quadrilateralABCDhas the property thatABandCDare congruent and parallel. Is this enough infor-mation to prove thatABCDis a parallelogram? Explain....ABEA0CD...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................August 201938Phillips Exeter Academy
Mathematics 2434.Suppose that squarePQRShas 15-cm sides, and thatGandHare onQRandPQ,respectively, so thatPHandQGare both 8 cm long. LetTbe the point wherePGmeetsSH. Find the size of angleSTG, with justification.435.(Continuation) Find the lengths ofPGandPT.436.There are four special types of lines associated with triangles: Medians, perpendicularbisectors, altitudes, and angle bisectors.(a)Which of these linesmustgo through the vertices of the triangle?(b)Is it possible for a median to also be an altitude? Explain.

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