TriangleCongruenceusingSSS
LearningObjectives
- Use the distanceformulato analyzetriangleson a coordinategrid.
- Understandand applythe SSS postulateof trianglecongruence.
Introduction
In the last sectionyou learnedthat if two trianglesare congruentthen the threepairsof correspondingsides
are congruentand the threepairsof correspondinganglesare congruent.In symbols,
means , and.
Wow, that’s a lot of information—infact, one trianglecongruencestatementcontainssixdifferentcongruence
statements!In this sectionwe showthat provingtwo trianglesare congruentdoesnot necessarilyrequire
showingall six congruencestatementsare true. Luckyfor us, thereare shortcutsfor showingtwo triangles
are congruent—thissectionand the next exploresomeof theseshortcuts.
Triangleson a CoordinateGrid
To beginlookingat rulesof trianglecongruence,we can use a coordinategrid. The followinggrid shows
two triangles.
The first step in findingout if thesetrianglesare congruentis to identifythe lengthsof the sides.In algebra,
you learnedthe distanceformula,shownbelow.
You can use this formulato find the distanceson the grid.
Example 1
Find the distancesof all the line segmentson the coordinategrid aboveusingthe distanceformula.Beginwith. First writethe coordinates.