Montana Math MT.CORE.GEOM.TRANS.3

MT.CORE.GEOM.TRANS.3 is a cluster heading. These are the individual standards under it.

• MT.CORE.GEOM.TRANS.3.a

  Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent, and

01

What Students Need to Do

Students decide whether one triangle can be moved, flipped, and resized by one scale factor to match another. They compare corresponding sides and angles, then explain why two matching angles guarantee a match.

02

What Mastery Looks Like

Students match the correct vertices, find the same ratio for all three side pairs, and check the corresponding angles. To justify AA, they align the side between two matching angles, dilate it to the right length, and show that the third vertices meet.

03

Common Misconceptions

Students may compare sides that do not correspond or check only one side ratio. Some think a dilation changes angles. Others think triangles with two matching angles must be the same size.

04

How to Assess It

Exit ticket: Two triangles each have angles of 40° and 70°. Explain how to move and dilate one to match the other, and state what must be true about their corresponding sides.

1. 01

   On grid paper, draw right triangles with legs 3 and 4, then 6 and 8; trace them and compare corresponding sides and angles.

2. 02

   Ask students to write why aligning and dilating the side between two matching angles makes the third vertices meet.

3. 03

   Give teams triangle cards labeled 3-4-5, 6-8-10, 5-5-6, and 10-10-12; have them pair similar triangles and find scale factors.

4. 04

   Print the same triangular logo at 100% and 150%; students measure sides and angles, then name the similarity transformation.

• 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 defi...