Side Length Quotients in Similar Triangles
5 min
Teacher Prep
Setup
Required Preparation
Narrative
In this activity, students identify whether two triangles are similar or not. Since no drawing is given, students will need to recognize that there is no single scale factor that multiplies all of the side lengths in one triangle to get the side lengths in the other triangle.
Launch
Provide access to geometry toolkits. Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Triangle A has side lengths 2, 3, and 4. Triangle B has side lengths 4, 5, and 6.
Is Triangle A similar to Triangle B? Be prepared to explain your reasoning.
Sample Response
No. Sample reasoning: The shortest side in Triangle A is doubled to get the shortest side in Triangle B, but the longest side in Triangle A is multiplied by 1.5 to get the longest side in Triangle B. Since the scale factor is not the same for all side lengths, the two triangles are not similar.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to make sure students understand that triangles cannot be similar if you cannot apply the same scale factor to each side of one triangle to get the corresponding sides of the other triangle. Discuss with students:
- “How can you tell if two figures are similar without drawing a diagram?” (Find a scale factor that takes the shortest side of one figure to the shortest side of the other figure. Test to see if the same scale factor works for all of the other sides.)
Display diagrams of the triangles for visual confirmation.
Anticipated Misconceptions
Some students may think that adding the same number to each side length will result in similar triangles. Draw a picture to help students see why this is not true.
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
10 min
20 min
Knowledge Components
All skills for this lesson
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Side Length Quotients in Similar Triangles
5 min
Teacher Prep
Setup
Required Preparation
Narrative
In this activity, students identify whether two triangles are similar or not. Since no drawing is given, students will need to recognize that there is no single scale factor that multiplies all of the side lengths in one triangle to get the side lengths in the other triangle.
Launch
Provide access to geometry toolkits. Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Triangle A has side lengths 2, 3, and 4. Triangle B has side lengths 4, 5, and 6.
Is Triangle A similar to Triangle B? Be prepared to explain your reasoning.
Sample Response
No. Sample reasoning: The shortest side in Triangle A is doubled to get the shortest side in Triangle B, but the longest side in Triangle A is multiplied by 1.5 to get the longest side in Triangle B. Since the scale factor is not the same for all side lengths, the two triangles are not similar.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to make sure students understand that triangles cannot be similar if you cannot apply the same scale factor to each side of one triangle to get the corresponding sides of the other triangle. Discuss with students:
- “How can you tell if two figures are similar without drawing a diagram?” (Find a scale factor that takes the shortest side of one figure to the shortest side of the other figure. Test to see if the same scale factor works for all of the other sides.)
Display diagrams of the triangles for visual confirmation.
Anticipated Misconceptions
Some students may think that adding the same number to each side length will result in similar triangles. Draw a picture to help students see why this is not true.
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.