Read the Vertex Order in a Congruence Statement
The written order in triangle ABC congruent to DEF pairs A with D, B with E, and C with F.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: Given triangle ABC congruent to triangle DEF in that order, AB=7, BC=8, AC=9. Find EF. Candidate answers: (A) 15 (B) 7 (C) 8 (D) 9.
- Independent check inputs: Given triangle ABC congruent to triangle DEF in that order, AB=8, BC=9, AC=10. Find EF. Candidate answers: (A) 10 (B) 17 (C) 8 (D) 9.
Learn the idea
Congruence fixes a figure’s shape and size, while correspondence identifies matching vertices and sides. Perpendicular and angle bisectors encode equidistance or equal-angle properties that can be used and checked in a construction. The written order in triangle ABC congruent to DEF pairs A with D, B with E, and C with F. Matching side endpoints then identifies the equal corresponding side.
Here is the method on the supplied teaching case. The ordered correspondence is A↔D, B↔E, C↔F. Thus EF corresponds to BC, not AB or AC; EF=8.
Do not match sides by where they appear on a sketch. Follow both endpoint correspondences; changing the vertex order changes what the statement asserts even when the pictures look similar.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: Given triangle ABC congruent to triangle DEF in that order, AB=7, BC=8, AC=9. Find EF. Candidate answers: (A) 15 (B) 7 (C) 8 (D) 9. Solution: The ordered correspondence is A↔D, B↔E, C↔F. Thus EF corresponds to BC, not AB or AC; EF=8. The final answer is 8. Do not match sides by where they appear on a sketch. Follow both endpoint correspondences; changing the vertex order changes what the statement asserts even when the pictures look similar.
Check your reasoning
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Helpful tips
- The written order in triangle ABC congruent to DEF pairs A with D, B with E, and C with F.
- Do not match sides by where they appear on a sketch.
See the answer and explanation
9
The ordered correspondence is A↔D, B↔E, C↔F. Thus EF corresponds to BC, not AB or AC; EF=9.
Take it further
Changed-input task: Given triangle ABC congruent to triangle DEF in that order, AB=14, BC=15, AC=16. Find EF. Candidate answers: (A) 14 (B) 15 (C) 16 (D) 29. Show the mathematical reason, not only the selected answer. Expected result: 15. The ordered correspondence is A↔D, B↔E, C↔F. Thus EF corresponds to BC, not AB or AC; EF=15.
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