Establish Triangle Congruence with Three Sides

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Triangles have matching side lengths 2, 3, 4, and 2, 3, 4. Which criterion establishes congruence? Candidate answers: (A) AAA (B) Equal perimeter alone (C) SSA in every triangle (D) SSS.
• Independent check inputs: Triangles have matching side lengths 3, 4, 5, and 3, 4, 5. Which criterion establishes congruence? Candidate answers: (A) AAA (B) Equal perimeter alone (C) SSA in every triangle (D) SSS.

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. Matching all three corresponding side lengths establishes triangle congruence through SSS. The triangles may be positioned or reflected differently while retaining identical shape and size.

Here is the method on the supplied teaching case. Three corresponding side lengths match, which is SSS. Equal angles establish similarity, while equal perimeter alone does not determine shape. The supplied lengths satisfy triangle inequality because 2+3>4.

A matching perimeter alone does not match individual sides. Equal angles establish similarity rather than size; list the side correspondences and confirm the supplied lengths form valid triangles.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Changed-input task: Triangles have matching side lengths 9, 10, 11, and 9, 10, 11. Which criterion establishes congruence? Candidate answers: (A) AAA (B) Equal perimeter alone (C) SSA in every triangle (D) SSS. Show the mathematical reason, not only the selected answer. Expected result: SSS. Three corresponding side lengths match, which is SSS. Equal angles establish similarity, while equal perimeter alone does not determine shape. The supplied lengths satisfy triangle inequality because 9+10>11.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.