.geometry "version 0.31";
.l0; 
v1 = .free(-0.162736, 0.00760445, .dot, "B");
v2 = .free(0.247905, 0.00760445, .dot, "C");
l1 = .l.vv(v1, v2);
l2 = .l.vlperp(v1, l1, .in);
c1 = .c.vv(v1, v2, .in);
v3 = .v.lc(l2, c1, 1, .dot);
l3 = .l.vv(v3, v1);
l4 = .l.vlperp(v3, l3, .in);
l5 = .l.vlperp(v2, l1, .in);
v4 = .v.ll(l4, l5, .dot);
l6 = .l.vv(v3, v4);
l7 = .l.vv(v4, v2);
c2 = .c.vv(v2, v4, .in);
v5 = .v.lc(l1, c2, 2, .dot, "D");
l8 = .l.vv(v2, v5);
l9 = .l.vlperp(v5, l8, .in);
v6 = .v.ll(l6, l9, .dot);
l10 = .l.vv(v4, v6);
l11 = .l.vv(v6, v5);
v7 = .v.lc(l1, c1, 1, .dot, "A");
l12 = .l.vv(v7, v1);
l13 = .l.vlperp(v7, l12, .in);
v8 = .v.ll(l13, l4, .dot, "E");
l14 = .l.vv(v8, v7);
l15 = .l.vv(v8, v3);
l16 = .l.vv(v8, v1);
l17 = .l.vv(v8, v2);
l18 = .l.vv(v8, v5);
ang1 = .a.vvv(v8, v1, v7);
ang2 = .a.vvv(v8, v2, v7, .ring2);
ang3 = .a.vvv(v8, v5, v7, .ring3);
.text("Given three squares as shown, show
that \angleABE + \angleACE + \angleADE = 90\degrees.", .l0);
c3 = .c.vv(v8, v3, .in, .l1);
v9 = .v.lc(l13, c3, 1, .in, .dot);
l19 = .l.vv(v9, v8, [.in, .blink1, .white]);
l20 = .l.vlperp(v9, l13, .in, .l1);
v10 = .v.ll(l20, l9, [.in, .blink1, .white], .dot, "Y");
v11 = .v.ll(l5, l20, [.in, .blink1, .white], .dot, "X");
v12 = .v.ll(l2, l20, .in, .dot);
l21 = .l.vv(v12, v3, [.in, .blink1, .white]);
l22 = .l.vv(v11, v4, [.in, .blink1, .white]);
l23 = .l.vv(v10, v6, [.in, .blink1, .white]);
l24 = .l.vv(v9, v10, [.in, .blink1, .white]);
.text("Construct three more squares as shown,
and connect the point labellel X with E and D.", .l1);
l25 = .l.vv(v8, v11, [.in, .blink, .white]);
l26 = .l.vv(v11, v5, [.in, .blink, .white]);
.text("\angleEXD is a right angle and
EX = XD, so \angleXDE = \angle EBA = 45\degrees.", .l2);
ang4 = .a.vvv(v11, v5, v8, [2 .in, .blink, .white]);
.text("\triangleYDX \congruent \triangleACE so
\angleYDX = \angle ACE.", .l3);
ang5 = .a.vvv(v10, v5, v11, [3 .in, .blink, .white], .ring2);
.text("It is clear from the picture that
\angleABE + \angleACE + \angleADE
= \angleYDX + \angle XDE + \angle EDA = 90\degrees.", .l4);
.text("Press 'Next' to continue ...", .red, .tol3);