Geometry: An Interactive Journey to Mastery



Solutions

10. +ANM is similar to +ABC by SAS with scale factor k = 2. The area of +ANM is^1  the area of +ABC.
    The same is true for ++CMOand BON.
    7KXVWKHQRQVKDGHGUHJLRQVUHSUHVHQW^3  of the area of the triangle, and the shaded region represents just^1 .
    The probability that the chosen point lies in this shaded region is thus^1 .
    Lesson 26


11. D௘ͽDQGE௘ͽͼ௘&RQVWUXFWLQJDVTXDUHFRQVWUXFWVDUHFWDQJOH௘ͽ
    Draw a line and a line segment AB along it.
    Using a circle of radius AB and center A, mark a point Bc on the line
    so that ABc = AB, as shown in Figure S.26.1.
    Drawing two circles, each of radius BBc, one with center B
    and the other with center Bc, gives two intersecting points
    WKDWGH¿QHDSHUSHQGLFXODUOLQHWKURXJKA, as shown
    in Figure S.26.2.
    Using A as the center and a circle of radius AB, mark a point C
    along the perpendicular segment, as shown in Figure S.26.3.
    We now have two sides of a square.
    Turn the page 90° and repeat this work starting with line
    segment CA to construct a perpendicular segment through C
    to make the third side of the square. Connect the ends of the
    ¿UVWDQGWKLUGVLGHVWRGUDZWKHIRXUWKHGJHRIWKHVTXDUH

Bc AB

Figure S.26.1

Bc AB

Figure S.26.2

A

C

Bc B

Figure S.26.3