Student Actions

Teacher Actions

• Develop a deep and flexible conceptual understanding by using triangle similarity postulates and theorems (AA, SSS, SAS) to construct logical arguments and proofs.

• Develop mathematical reasoning by explaining the difference between triangle congruence and similarity and the connection to similar and congruent polygons.

• Develop the ability to communicate mathematically by explaining which corresponding parts of triangles are similar and how to calculate the ratio of the corresponding parts. 

• Promote reasoning and problem-solving by implementing tasks that allow students to explore and develop multiple methods of proving triangles similar.

• Support productive struggle by providing a variety of tasks that encourage student independence.

• Pose purposeful questions by guiding students to construct logical arguments and proofs.

• Elicit and use evidence of student understanding by encouraging discussions and group practice constructing logical arguments to prove the similarity of triangles.

• Use and connect mathematical representations by modeling logical arguments and proofs using similar triangle postulates and theorems.

• Encourage the use of technology when available. 

Key Understandings

Misconceptions 

• Prove triangles are similar by accurately applying AA, SSS, or SAS 

• Identify the ratio of similar, corresponding sides and use the ratio to calculate unknown side measurements. 

• Two-column or paragraph proofs are used to organize reasons and statements to prove triangle similarity.

• The angles of similar triangles remain the same measure, but the side lengths have the same ratio or scale factor. 

• Students confuse the basic concepts of similarity and congruence.

• Students try to use SSA as a method to prove triangles are similar.

• Students have trouble understanding the terms “included angle”, “included side”, “non-included angle” and “non-included side”.

• Students may incorrectly identify corresponding sides and/or angles of similar triangles

• Students may incorrectly determine the scale factor and/or incorrectly identify an appropriate ratio of corresponding sides. 

• Students may not understand that angle measures remain the same and may try to calculate an angle’s ratio or scale factor

• Students may not correctly identify reasons and/or statements and/or understand the process for constructing two-column proofs.

• Students may understand how to construct logical arguments, but may not be able to explain their reasoning. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Students were introduced to the concepts of similarity and scale factor in middle school.

• Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs. (G.RL.1.1)

• Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. (G.RL.1.2) 

• Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning. (G.2D.1.8) 

• Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume. (G.3D.1.2) 

• Create models for situations involving trigonometry. (PC.T.2.1)