Lesson Plan: Congruence and Similarity of Geometric Figures
Description:Students will explore congruent and similar figures by creating polygons using internet resources and applets. Students will share their observations by comparing and contrasting figures and sharing with peers, table groups and whole class discussions. Technology Required:
Internet access.
Students will have 1:1 access to chrome books.
Sites require flash and may need to be installed on chrome browsers.
AUP/FERPA - Geogebra requires students to create a username in order to save their work. Check with your school district and AUP before permitting students to create a username. This lesson was created without having students create a login.
Learning Target: Know that two objects are similar if their corresponding sides are proportional and their angles are congruent.
Entry event: Students will use a virtual geoboard (11x11) https://illuminations.nctm.org/Activity.aspx?id=6385 to create multiple polygons including a square, triangle and quadrilaterals (Requires Adobe flash)
Success Criteria: Students will be able to use geometry software using an applet to create similar polygons. Students will be asked to complete four (4) problems at the end of this lesson as a formative assessment. https://www.geogebra.org/m/dzZmcjxN#material/XmpN7gMb
Congruent - equal size and measure of a geometric shape
Similar - same shape but not same size.
Polygon - A 2D closed geometric shape
Quadrilateral - a polygon with 4 sides
Additional Vocabulary
Geoboard - rectangular or triangular grid with pegs which form vertices to create polygons
nodes - the “peg” of the geoboard
Tilde - similarity symbol~
Task 1 Students will use the internet tool of a virtual 11x11 geoboard at https://illuminations.nctm.org/Activity.aspx?id=6385. Ask students to explore geometric shapes and measurements and suggest they try shading areas, hiding pegs, deleting segments, and moving vertices.
Students will begin by creating a triangle, square, rectangle, quadrilateral, polygon of their choosing. To engage students, ask them to try to create a polygon with as few sides as possible and then create a polygon with the largest numbers of sides as possible.
When students are comfortable with task of creating shapes on the virtual geoboard, ask students to each create two (2) triangles. Have them explain to a friend the ways in which these triangles are different and how they are alike. Some students may come up with idea such as:
congruent triangles - same angles, same side lengths
Similar triangles - same angles, different side lengths
Non-congruent and non similar triangles.
Whole class discussion: use student examples to compare and contrast shapes. Use teacher projection software to project student images onto the screen for discussion.
Part 2 - Identify Similar Figures
Task 2 Students will use the internet tool at: https://www.geogebra.org/geometry Begin the lesson by allowing students to explore the tool including:
Learn how to make right triangle
Learn how to label a triangle vertices
Use measure tool to measure angles
Turn on the grid
Learn to snap to grid
Ask students to make a two right triangles which are similar:
Triangle (ABC) with a base of 1 and a height of 2
Triangle (DEF) with a base of 3 and a height of 6
Label the vertices and measure the angles. Discuss what makes these similar? Same angles measures (congruent angles) and proportional side lengths. Use text box to write the similarity statements AB ~DE and BC~EF and AC~DF
Give students time to explore making additional similar triangles. Ask students to describe how their shapes are similar and encourage students to use academic vocabulary and similarity statements.
Formative Assessment: Students will be asked to complete four (4) problems aligned to the learning target at the end of this lesson as a formative assessment. https://www.geogebra.org/m/dzZmcjxN#material/XmpN7gMb
Intervention/Remediation: struggling students will be placed into small groups or 1:1 for reteaching
Extension Activity: Using a rectangle - Explore the similarity of the perimeters. Ask the question "Does the proportion of similarity work for perimeters?". Students can begin exploring dilation with the applet https://www.geogebra.org/m/cGNwUnFC