Montana Math MT.CORE.GEOM.TRANS.2.b
The Standard
- MT.CORE.GEOM.TRANS.2
- Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by: Using the definition of congruence in terms of rigid motions to show that two triangles are congruent if, and only if, corresponding pairs of sides and corresponding pairs of angles are congruent, and Verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).
Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by: Verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).
2026 Montana Mathematics Content Standards · Geometric Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students match corresponding sides and angles in two triangles. They use ASA, SAS, or SSS to show the triangles are congruent, then use slides, turns, or flips to place one over the other.
What Mastery Looks Like
- Students identify the included angle in SAS and the included side in ASA. They match every vertex and describe rigid motions that place one triangle exactly over the other.
Common Misconceptions
- Students often think AAA or SSA guarantees congruence. They may use a nonincluded angle for SAS or match the wrong vertices.
How to Assess It
- Exit ticket: Triangle ABC has A(0,0), B(3,0), C(0,4); triangle DEF has D(5,1), E(8,1), F(5,5). Name the motion mapping ABC onto DEF and justify congruence with SAS using matching parts.
Lesson moves
Ways to Teach It
Cut out two labeled triangles, trace one on clear plastic, and slide, turn, or flip it until corresponding vertices line up.
Sketch two triangles with sides 7 cm and 10 cm and a 30° angle opposite the 7 cm side; explain any differences.
Give pairs cards showing triangles marked ASA, SAS, SSS, SSA, or AAA; have them sort guaranteed matches from possible mismatches.
Give students a printed quilt block with matching triangular patches; have them mark the slide, turn, or flip connecting two patches.
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