Similar Triangles
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to make sense of a figure by considering properties of triangles and similar polygons. This figure is also used in the optional activity.
Launch
Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Introduce the context image from the task. Use Co-Craft Questions to orient students to the context and elicit possible mathematical questions.
Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.
Student Task
Sample Response
Sample responses:
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What is the measure of angle JDI?
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What is the measure of angle IHC?
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What is the measure of angle JFG?
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Which triangles are similar to triangle HIC?
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Which triangles in this picture are similar?
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Which triangles in this picture are congruent?
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How many triangles are in this picture?
Activity Synthesis (Teacher Notes)
Invite several partners to share 1 question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?”
If questions about similarity or scale factor are not mentioned by students, ask students "What is a mathematical question about similar figures that you could ask using this diagram?"
Standards
- 8.G.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.A.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.5·Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. <em>For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.</em>
- 8.G.A.5·Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. <span>For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.</span>
30 min
Knowledge Components
All skills for this lesson
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Similar Triangles
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to make sense of a figure by considering properties of triangles and similar polygons. This figure is also used in the optional activity.
Launch
Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Introduce the context image from the task. Use Co-Craft Questions to orient students to the context and elicit possible mathematical questions.
Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.
Student Task
Sample Response
Sample responses:
-
What is the measure of angle JDI?
-
What is the measure of angle IHC?
-
What is the measure of angle JFG?
-
Which triangles are similar to triangle HIC?
-
Which triangles in this picture are similar?
-
Which triangles in this picture are congruent?
-
How many triangles are in this picture?
Activity Synthesis (Teacher Notes)
Invite several partners to share 1 question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?”
If questions about similarity or scale factor are not mentioned by students, ask students "What is a mathematical question about similar figures that you could ask using this diagram?"
Standards
- 8.G.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.A.4·Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
- 8.G.5·Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. <em>For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.</em>
- 8.G.A.5·Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. <span>For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.</span>