Practice with Recognizing Congruent Triangles Topic Index | Geometry Index | Regents Exam Prep Center

Now that you know the methods for proving triangles congruent, let's practice using these methods.  For the following problems, copy the diagram onto a piece of paper, and mark up the diagram with the given information.  Choose the method for proving triangles congruent that should be used based upon the information given or shown in each problem.  If there is not enough information to prove the triangles congruent, choose "Not Possible" (NP).

(NP ==>  Not Possible to prove congruent triangles with the information given.)

1.

 SAS ASA SSS AAS HL NP Hint This problem is a straight forward example of ASA. All of the needed parts were supplied in the GIVEN.

2.

 SAS ASA SSS AAS HL NP Hint Did you notice that the triangles share a side? Side BD (reflexive) becomes the third component in proving the triangles congruent by SSS.

3.

 SAS ASA SSS AAS HL NP Hint Did you notice that the triangles share side RT? With side RT (reflexive) the triangles are congruent by SAS.

4.

 SAS ASA SSS AAS HL NP Hint This is a trickly one! Look out! It is true that the two triangles LOOK like right triangles, but you are not told that this is the case. DO NOT assume right triangles. There are NO right angles and there is insufficient information to prove the triangles congruent.

5.

 SAS ASA SSS AAS HL NP Hint The perpendiculars form right angles Thus we have two right triangles. The right triangles share side RP (reflexive), which serves as the hypotenuse for both triangles. We now have HL for right triangles.

6.

 SAS ASA SSS AAS HL NP Hint Beware! There is NO information in this problem about the sides. You know NOTHING about the sides. There is insufficient information in this problem.

7.

 SAS ASA SSS AAS HL NP Hint The bisector forms two sets of congruent angles. The triangles share side KT. We have ASA.

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