ACT Preparation / Unit 13 ACT 1215 worked example, 60 to 90 seconds
Which Triangles Are Congruent
The idea
To decide whether two triangles are congruent, work in three steps. First, list the matching parts the figure gives, including shared sides and vertical angles, which are equal without being marked. Second, check whether they fit a valid test: SSS, SAS, ASA, AAS, or hypotenuse-leg for right triangles, rejecting SSA and AAA. Third, if the triangles are congruent, write the statement in corresponding order and use it to transfer a missing measure.
In practice
Worked example: segments AD and BC cross at E, with AE = DE and BE = CE. The angles at E, AEB and DEC, are vertical angles, so they are equal. Two sides and the angle between them match, so triangle AEB ≅ triangle DEC by SAS. Then AB = DC, so if AB is 9, DC is 9.
Where people slip
A shared side or a pair of vertical angles is a given that the figure does not label. Count it before deciding the triangles cannot be proved congruent.
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