# Proportion and Similarity HSG.SRT.A.2

This learning progression is provided to support student’s understanding of ratios and proportionality in relation to similar figures. There is a series of three consecutive math tasks that will be completed by students to help guide them through using ratios and proportions to prove figures are similar.

Students will use their knowledge of algebra to express proper ratios and simplify them correctly. They will also be using the cross product of ratios to solve the proportions.

• MATH.CONTENT.HSA.SSE.B.3-Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Students will identify congruent angles and corresponding sides of a polygon so they can find the similarity ratio. Once they do this, they will be able to recognize the sides and angles that are proportional and determine if polygons are similar.

• MATH.CONTENT.HSG.SRT.A.2-Given two figures, use the definition of
similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Students will use triangle similarity theorems to show how congruent angles and corresponding sides that are proportional determine if triangles are similar.

• MATH.CONTENT.HSG.SRT.A.3-Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Formative assessment in the form of observation and discussion will be the primary procedure to support student learning. I will observe how they are finding solutions and ask them questions about their understanding of the learning targets.  At the end of each task students will be given a handout, which will also show how well they are able to meet the learning targets.

Proportion and Similarity Learning Progression