Montana Math MT.CORE.GEOM.TRANS.3.a
The Standard
- MT.CORE.GEOM.TRANS.3
- Define the similarity of two figures in terms of similarity transformations by: Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent, and Using the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.
Define the similarity of two figures in terms of similarity transformations by: Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent, and
2026 Montana Mathematics Content Standards · Geometric Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students match the corners of two triangles, compare side ratios, and check angles. They explain how a dilation and slides, turns, or flips can map one triangle onto the other.
What Mastery Looks Like
- A student can find a dilation and a slide, turn, or flip that maps one triangle onto another when corresponding sides are proportional and angles match. They can also use that map to explain why the side ratios match and the angles stay equal.
Common Misconceptions
- Students may compare sides in the wrong order or think similar triangles need equal side lengths. Some think a dilation changes angles, or that matching side ratios cannot tell them anything about angles.
How to Assess It
- Exit ticket: Triangles have vertices (0,0), (3,0), (0,4) and (1,1), (7,1), (1,9). Name a dilation and translation that map the first onto the second, then explain what happens to corresponding sides and angles.
Lesson moves
Ways to Teach It
On grid paper, draw a 3-4-5 triangle, dilate it from a marked center by a factor of two, then measure matching angles.
Show triangles with sides 3, 4, 5 and 6, 8, 10; ask, "How can we know their angles match without measuring them?"
Give pairs of triangle cards with side lengths and angle measures; students match similar pairs and record the vertex order and scale factor.
Hand out scale drawings of two triangular road signs; ask students to find the scale factor and show how one maps onto the other.
Keep exploring
Related Standards
- MT.CORE.GEOM.ARG.1.b
Proving theorems about triangles. Theorems include: the sum of the measures of the interior angles of a triangle is 180˚, the Pythagorean Theorem, the base angl...
- MT.CORE.GEOM.TRANS.2.b
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-si...
- MT.CORE.GEOM.TRANS.3
Define the similarity of two figures in terms of similarity transformations by: Verifying that two triangles are similar if, and only if, corresponding pairs of...
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