- If thereare multiplepairsof congruentsegments(whichare not congruentto eachother)in the same
picture,use two tic marksfor the secondset of congruentsegments,threefor the third set, and so on.
See the two followingillustrations.
Recallthat the lengthof segment can be writtenin two ways: or simply. This mightbe
a little confusingat first, but it will makesenseas you use this notationmoreand more.Let’s say we used
a ruler and measured and we saw that it had a lengthof 5 cm. Thenwe couldwrite cm,
or cm.
If we knowthat , then we can write or simply.
You can provetwo segmentsare congruentin a numberof ways.You can measurethemto find their lengths
usingany unitsof measurement—theunitsdo not matteras long as you use the sameunitsfor both mea-
surements.Or, if the segmentsare drawnin the plane,you can also find their lengthson the coordinate
grid. Laterin the courseyou will learnotherwaysto provetwo segmentsare congruent.
Example 1
Henriettadrewa line segmenton a coordinategrid as shownbelow.She wantsto drawanothersegmentcongruentto the first that beginsat (-1,1)and travelsstraightup (that
is, in the
direction).Whatwill be the coordinatesof its secondendpoint?
You will haveto solvethis problemin stages.The first step is to identifythe lengthof the segmentdrawn
onto the grid. It beginsat (2,3) and endsat (6,3).So, its lengthis 4 units.