Practice with Beginning Congruent Triangle Proofs Topic Index | Geometry Index | Regents Exam Prep Center

Directions:  When attempting to prove triangles congruent, it is important to satisfy all of the conditions of the congruent triangle method you are using.  This activity is designed to help you organize your thinking about how the parts of a congruent triangle proof will come together.  In each problem below, examine the diagram and the GIVEN information.  You may wish to draw the diagrams on paper so that you can mark off the information.

• Determine the method needed to prove the triangles congruent.
(ASA, SAS, AAS, SSS, or HL for right triangles only)

• Check to see if you have the correct method by looking at the Method for Congruent Triangles box at the bottom of the chart.

• Each of the three components needed to support the chosen method appear to the left of their corresponding Statement.

• Decide what Reasons can be used to support your decisions.

 This first problem is an easy problem designed to let you see how this activity is going to work.  Look carefully at the problem before continuing.  If you click on the answer in the drop down box, it will remain visible.

 1
 Method Statements Reasons ??? S 1. Reason Given ??? A 2. Reason Given ??? S 3. Reason Given 4. Method for Congruent Triangles SAS congruent SAS

 2
 Method Statements Reasons ??? S 1. Reason Midpoint of a segment divides the segment into two congruent segments. ??? A 2. Reason Vertical angles are congruent. ??? S 3. Reason Given 4. Method for Congruent Triangles SAS congruent SAS

 3
 Method Statements Reasons ??? A 1. Reason Given ??? A 2. Reason Given ??? S 3. Reason Reflexive property (shared side) 4. Method for Congruent Triangles AAS congruent AAS

 4
 Method Statements Reasons ??? A 1. Reason Given ??? S 2. Reason Midpoint of segment divides the segment into two congruent segments. ??? A 3. Reason Given 4. Method for Congruent Triangles ASA congruent ASA

 5
 Method Statements Reasons ??? S 1. Reason Given 2. Reason Bisector of a segment intersects the segment at its midpoint. ??? S 3. Reason Midpoint of a segment divides the segment into two congruent segments. ??? S 4. Reason Midpoint of a segment divides a segment into two congruent segments. 5. Method for Congruent Triangles SSS congruent SSS

(Problem #5 could also have been solved using SAS and the vertical angles.)

 6
 Method Organized Thinking Supporting Reason 1. Reason Given ??? Rt. Tri. 2. Reason A right triangle contains one right angle. ??? H 3. Reason Given ??? L 4. Reason Reflexive Property (shared side) 5. Method for Congruent Triangles HL congruent HL (for Right Triangles)

(Be careful with problem #6.
Remember that ASS (the Donkey Theorem) does not work to prove triangles congruent.)

 In each of these problems,  the 3 components of each congruent triangle method actually APPEARED in the proof.  For example, if SAS was used, the proof contained two sets of congruent sides (S, S) and one set of congruent angles (A). Be sure you satisfy all 3 parts of the method you are using, BEFORE you state that your triangles are congruent.

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