random() < 0.5 ? "Yes" : "No"
sortNumbers( randRangeUnique( -5, 5, 4 ) )
[ BLUE, GREEN, PINK, ORANGE ]

Are \overline{AB} and \overline{CD} congruent?

init({ range: [ [ -6, 6 ], [ -1, 1 ] ] }); style({ stroke: "#999" }); line( [ -5, 0 ], [ 5, 0 ] ); for ( var x = -5; x <= 5; x++ ) { line( [ x, -0.2 ], [ x, 0.2 ] ); label( [ x, -0.53 ], String( x ).replace( /-(\d)/g, "\\llap{-}$1" ), "center", { color: "#999" } ); } style({ strokeWidth: 3.5 }); line( [ 0, -0.2], [0, 0.2]); style({ stroke: COLORS[ 0 ], fill: COLORS[ 0 ] }); circle( [ POINTS[ 0 ], 0 ], 0.10 ); style({ stroke: COLORS[ 1 ], fill: COLORS[ 1 ] }); circle( [ POINTS[ 1 ], 0 ], 0.10 ); style({ stroke: COLORS[ 2 ], fill: COLORS[ 2 ] }); circle( [ POINTS[ 2 ], 0 ], 0.10 ); style({ stroke: COLORS[ 3 ], fill: COLORS[ 3 ] }); circle( [ POINTS[ 3 ], 0 ], 0.10 ); label( [ POINTS[ 0 ], 0 ], "A", "above", { color: COLORS[ 0 ] } ); label( [ POINTS[ 1 ], 0 ], "B", "above", { color: COLORS[ 1 ] } ); label( [ POINTS[ 2 ], 0 ], "C", "above", { color: COLORS[ 2 ] } ); label( [ POINTS[ 3 ], 0 ], "D", "above", { color: COLORS[ 3 ] } );
SOLUTION
  • Yes
  • No

Congruent segments have equal lengths.

Find the lengths of \overline{AB} and \overline{CD}:

AB = |\color{COLORS[ 0 ]}{POINTS[ 0 ]} - \color{COLORS[ 1 ]}{POINTS[ 1 ]}| CD = |\color{COLORS[ 2 ]}{POINTS[ 2 ]} - \color{COLORS[ 3 ]}{POINTS[ 3 ]}|

AB = |POINTS[ 0 ] - POINTS[ 1 ]| CD = |POINTS[ 2 ] - POINTS[ 3 ]|

AB = POINTS[ 1 ] - POINTS[ 0 ] CD = POINTS[ 3 ] - POINTS[ 2 ]

AB = CD

Yes, \overline{AB} and \overline{CD} are congruent.

AB \neq CD

No, \overline{AB} and \overline{CD} are not congruent.