<?xml version="1.0" encoding="utf-8"?>
<!-- Geometry Snacks #29 (Prove it!), drawn by hand as a ruler-and-compass construction.
     The figure is rigid: the three tick-marked segments are equal, the two small squares meet at the vertex V at 45°
     (the shaded one is tilted, the white one upright), and that fixes the white square's side as the shaded square's
     diagonal. A handle could only turn the figure, so nothing is dragged: P1, the shaded square's bottom vertex, is a
     hidden point below and to the left of V, as the book has it. The shaded square stands on P1V (perpendiculars
     and circles); the white square's far corner P3 is the mirror image of the shaded square's left vertex through V
     (the diagonal through V carried on); the white square stands on VP3. P4 is the fourth vertex of the parallelogram
     P1 V P3 P4 (V reflected through the midpoint of P1P3), so VP4 = P4P3 = P1V. The red square stands on P1P3. -->
<Drawing Version="1">
  <Viewport Left="-5.2" Top="5.2" Right="5.2" Bottom="-5.2" />
  <Scene Left="-5.2" Top="5.2" Right="5.2" Bottom="-5.2" />
  <Styles>
    <ShapeStyle Name="Frame" Color="#FF000000" StrokeWidth="3" IsFilled="false">
      <Dark Color="#FFE8EBF0" />
    </ShapeStyle>
    <ShapeStyle Name="RedFrame" Color="#FFEF303F" StrokeWidth="3" IsFilled="false">
      <Dark Color="#FFF0616C" />
    </ShapeStyle>
    <ShapeStyle Name="Grey" Color="#FF000000" StrokeWidth="3" Fill="#FFC8C8C8">
      <Dark Color="#FFE8EBF0" Fill="#FF6B7280" />
    </ShapeStyle>
    <LineStyle Name="Ink" Color="#FF000000" StrokeWidth="3">
      <Dark Color="#FFE8EBF0" />
    </LineStyle>
  </Styles>
  <Figures>
    <FreePoint Name="V" Visible="false" Locked="true" X="0" Y="0" />
    <FreePoint Name="P1" Visible="false" Locked="true" X="-1.13137" Y="-1.13137" />
    <!-- the shaded square on P1V, to the left of the way from P1 to V -->
    <Segment Name="P1V" Visible="false">
      <Dependency Name="P1" />
      <Dependency Name="V" />
    </Segment>
    <PerpendicularLine Name="atV" Visible="false">
      <Dependency Name="P1V" />
      <Dependency Name="V" />
    </PerpendicularLine>
    <PerpendicularLine Name="atP1" Visible="false">
      <Dependency Name="P1V" />
      <Dependency Name="P1" />
    </PerpendicularLine>
    <Circle Name="cV" Visible="false">
      <Dependency Name="V" />
      <Dependency Name="P1" />
    </Circle>
    <Circle Name="cP1" Visible="false">
      <Dependency Name="P1" />
      <Dependency Name="V" />
    </Circle>
    <IntersectionPoint Name="Q3" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="atV" />
      <Dependency Name="cV" />
    </IntersectionPoint>
    <IntersectionPoint Name="Q4" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="atP1" />
      <Dependency Name="cP1" />
    </IntersectionPoint>
    <Polygon Name="Shaded" Style="Grey">
      <Dependency Name="P1" />
      <Dependency Name="V" />
      <Dependency Name="Q3" />
      <Dependency Name="Q4" />
    </Polygon>
    <!-- the white square on VP3, where P3 is Q4 reflected through V, to the left of the way from V to P3 -->
    <ReflectedPoint Name="P3" Visible="false">
      <Dependency Name="Q4" />
      <Dependency Name="V" />
    </ReflectedPoint>
    <Segment Name="VP3" Visible="false">
      <Dependency Name="V" />
      <Dependency Name="P3" />
    </Segment>
    <PerpendicularLine Name="whiteAtV" Visible="false">
      <Dependency Name="VP3" />
      <Dependency Name="V" />
    </PerpendicularLine>
    <PerpendicularLine Name="whiteAtP3" Visible="false">
      <Dependency Name="VP3" />
      <Dependency Name="P3" />
    </PerpendicularLine>
    <Circle Name="cVwhite" Visible="false">
      <Dependency Name="V" />
      <Dependency Name="P3" />
    </Circle>
    <Circle Name="cP3" Visible="false">
      <Dependency Name="P3" />
      <Dependency Name="V" />
    </Circle>
    <IntersectionPoint Name="W1" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="whiteAtV" />
      <Dependency Name="cVwhite" />
    </IntersectionPoint>
    <IntersectionPoint Name="W2" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="whiteAtP3" />
      <Dependency Name="cP3" />
    </IntersectionPoint>
    <Polygon Name="White" Style="Frame">
      <Dependency Name="V" />
      <Dependency Name="P3" />
      <Dependency Name="W2" />
      <Dependency Name="W1" />
    </Polygon>
    <!-- the parallelogram P1 V P3 P4 and its three equal segments -->
    <MidPoint Name="Mid" Visible="false">
      <Dependency Name="P1" />
      <Dependency Name="P3" />
    </MidPoint>
    <ReflectedPoint Name="P4" Visible="false">
      <Dependency Name="V" />
      <Dependency Name="Mid" />
    </ReflectedPoint>
    <Segment Name="P1P4" Style="Ink">
      <Dependency Name="P1" />
      <Dependency Name="P4" />
    </Segment>
    <Segment Name="P1Vmark" Style="Ink" Decoration="TwoTicks">
      <Dependency Name="P1" />
      <Dependency Name="V" />
    </Segment>
    <Segment Name="VP4" Style="Ink" Decoration="TwoTicks">
      <Dependency Name="V" />
      <Dependency Name="P4" />
    </Segment>
    <Segment Name="P4P3" Style="Ink" Decoration="TwoTicks">
      <Dependency Name="P4" />
      <Dependency Name="P3" />
    </Segment>
    <!-- the red square on P1P3, to the right of the way from P1 to P3 -->
    <Segment Name="P1P3" Visible="false">
      <Dependency Name="P1" />
      <Dependency Name="P3" />
    </Segment>
    <PerpendicularLine Name="redAtP1" Visible="false">
      <Dependency Name="P1P3" />
      <Dependency Name="P1" />
    </PerpendicularLine>
    <PerpendicularLine Name="redAtP3" Visible="false">
      <Dependency Name="P1P3" />
      <Dependency Name="P3" />
    </PerpendicularLine>
    <Circle Name="cP1red" Visible="false">
      <Dependency Name="P1" />
      <Dependency Name="P3" />
    </Circle>
    <Circle Name="cP3red" Visible="false">
      <Dependency Name="P3" />
      <Dependency Name="P1" />
    </Circle>
    <IntersectionPoint Name="R1" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="redAtP1" />
      <Dependency Name="cP1red" />
    </IntersectionPoint>
    <IntersectionPoint Name="R2" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="redAtP3" />
      <Dependency Name="cP3red" />
    </IntersectionPoint>
    <Polygon Name="Red" Style="RedFrame">
      <Dependency Name="P1" />
      <Dependency Name="P3" />
      <Dependency Name="R2" />
      <Dependency Name="R1" />
    </Polygon>
  </Figures>
</Drawing>
