Understanding Similar Polygons and Scale Factors

Objective:

Students will be able to identify similar polygons, calculate scale factors between corresponding sides, and solve problems involving similar polygons.

Assessment:

Students will be provided with a worksheet containing different pairs of polygons and will need to determine if they are similar or not, calculate the scale factor between corresponding sides, and solve word problems based on the concept.

Key Points:

• Similar Polygons: Two polygons with the same shape, but not the same size. They have corresponding angles that are congruent and corresponding sides that are proportional.

• Corresponding Angles: Angles in similar polygons are congruent.

• Corresponding Sides: Sides in similar polygons are proportional.

• Scale Factor: The ratio of one side of a polygon to the corresponding side of the other. It is written in simplest form.

  • Formula: Scale Factor = Length of Side in Image / Length of Corresponding Side in Object

• Proportional Sides: In similar polygons, the lengths of corresponding sides are proportional.

  • Formula: If polygons are similar, then a/b = c/d, where a and c are corresponding sides of one polygon, and b and d are corresponding sides of the other.

Opening:

• Introduce the concept of similar polygons by showing two different polygons and asking students to identify if they are similar or not.

• Engage students by asking: "How can you tell if two shapes are similar?"

Introduction to New Material:

• Define similar polygons and explain the concept of corresponding angles and sides.

• Discuss the importance of proportional sides in similar polygons.

• Common Misconception: Students may think that similar polygons have the same size, clarify the difference.

Guided Practice:

• Provide examples of pairs of similar polygons for students to work through.

• Scaffold questioning from easy to hard to ensure understanding.

• Monitor student performance by circulating the room and checking their work.

Independent Practice:

• Assign a worksheet with various pairs of polygons for students to determine if they are similar, calculate scale factors, and solve problems.

• Ensure students show their work clearly and justify their answers.

Closing:

• Have students share their answers and discuss any challenges they faced.

• Summarize the key points of the lesson on the board.

Extension Activity:

• Challenge early finishers to create their own pairs of similar polygons and calculate the scale factor between corresponding sides.

Homework:

• For homework, students are to find examples of similar polygons in real-life situations and calculate the scale factor for one pair.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.A.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify the corresponding cross-sections of common three-dimensional objects.

• CCSS.MATH.CONTENT.HSG.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.