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# Applying Triangle Angle Theorems

Lesson 5 of 11

## Objective: SWBAT Apply triangle angle theorems to find the measures of missing angles

#### Do Now

*7 min*

In the Do Now, students are asked to identify numbered angles using letters. Students have difficulty identifying angles using letters. This activity allows students to practice correctly identifying angles and informs me of the students who need more practice or clarification. After about 4 minutes, we go over the angles and discuss the different ways the angles could be named.

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#### Mini-Lesson

*10 min*

The Mini-Lesson begins with a review of the terms **vertical angles**, **alternate interior angles**, and **linear pair**. Students identify angles of the diagram from the Do Now. Since there are multiple answers for each question, I call on multiple students to provide answers until we provide a relatively complete description of the angles in the diagram.

We then go over some angle theorems using angles from the diagram. I plan to have my students answer questions based on their knowledge of postulates and theorems. These questions will help them complete the activity later in the lesson.

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#### Activity

*23 min*

Applying Triangle Angle Theorems Activity asks students to interpret and use given information about a diagram. Using this information and their knowledge of theorems and postulates, students work together to figure out the measures of each of the angles in the diagram. After they find the measures of the angles, they apply their knowledge to answer questions about parts of the diagram.

Standard G.CO.10 states, "Prove theorems about triangles." Although this activity does not explicitly have students prove theorems, they are using theorems they proved in previous lessons.

Some students need additional guidance in order to answer these questions. I work with small groups to discuss the theorems needed. If students are still having difficulty, I provide them with an alternative activity to work on. This activity provides more scaffolding for these students.

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#### Summary

*5 min*

To end the lesson, we go over the measures of the angles in the diagram. I call on students to give the measures of angles and explain how they found the measure (MP3). We then discuss answers to the questions about the angles.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: Triangle Inequality Theorem Investigation
- LESSON 2: Side-Side-Side
- LESSON 3: Angles of Triangles
- LESSON 4: Relationships between Angles and Sides of a Triangle
- LESSON 5: Applying Triangle Angle Theorems
- LESSON 6: Side-Angle-Side
- LESSON 7: Angle-Side-Angle
- LESSON 8: CPCTC
- LESSON 9: Additional Properties of Triangles
- LESSON 10: Properties of Isosceles Triangles
- LESSON 11: Properties of Isosceles Triangles Alternative Lesson with Dynamic Geometry Software