Angle Relationships Lesson Plan - Kayla Kolbe~My Field Folio

Angle Relationships Lesson Plan

Sources/Text: Pearson--Geometry Common Core

Mathematical Goals and objectives; The student will investigate the relationships between angles formed by a pair of parallel lines and a transversal. The student will define and identify alternate interior angles, same-side interior angles, corresponding angles, and alternate exterior angles.

CCSS addressed: G.CO.1 Know precise definitions of...parallel lines (Prepares for) G.CO.9 Prove theorems about lines and angles. Theorems include: ...when a transversal crosses parallel lines, alternate interior angles are congruent...

Materials: Chromebooks, Geogebratube student page, "Angle Relationships" worksheet, vocabulary guide worksheet, parallel line/transversal diagram worksheet.

I. Engagement Block (Launch)

8 min

Overview: For the Warm-Up, students will state the relationships between vertical angles, complementary angles, supplementary angles, and a linear pair. After the Warm-Up and the relationships have been stated, every student needs a Chromebook. Have students go to the following link: This will take them to the student page Angle Properties of Parallel Lines.

Introduce the activity--tell students they will be exploring angles created by parallel lines and a transversal.

II. Cooperative Work Block

15-25 min

Overview: Students will work with a partner through the Angle Relationships activity. Only give student pairs Part 1 of the activity to start. Students should manipulate the student page to investigate what happens when the parallel lines and/or transversal are moved. They will write down any observations they notice about how the angles formed relate to one another. (Part 1 should take approximately 5-10 minutes).

Possible student observations for Part 1: There are eight angles. Each group of four angles makes a circle. When the lines move, the measures of the angles change. Some angles look like they are the same. Some angles are not the same. Angles that are right next to each other make up a line, which means they have to add up

to 180 degrees. Angles that are vertical always are congruent.

 All of the angles have the same measure when the transversal is perpendicular to the pair of parallel lines.

Possible student questions from Part 1: Q: Some angles are the same, but others are not. I don't understand what relationship I

am supposed to be seeing between those angles. o Response: Find two angles that don't seem to be congruent. Is there something else about those angles that you notice? Think about the angle pairs and relationships we have already discussed in previous lessons.

Q: I don't see anything. o Response: Let's choose an angle in the picture. Do you see any other angles that look similar to this angle? Do you see any other angles that look different than this angle? Why do you think is? What do you think the specific relationships between these angles are?

Once student pairs have finished Part 1, they are ready to begin Part 2.

Possible student observations for Part 2 (Part 2 should take approximately 15 minutes): Red and gray, and brown and green are both pairs of vertical angles, so they are congruent. But all four of them appear to be congruent as well. (Same for blue, black, pink and purple.) The linear pairs are angles that are right next to each other and form a line. Thus, these pairs are supplementary. However, other angles that are not linear pairs are also supplementary (such as blue and brown).

*Some students may struggle with understanding that angles can be both congruent and supplementary. If this is the case, have the manipulate the picture so all angles are 90 degrees.

III. Summary Block:

20-25 min

Overview: After students have completed the activity. Each student should receive a vocabulary guide and a parallel/transversal diagram . At this point in the lesson, students have not learned the vocabulary of alternate interior angles, alternate exterior angles, corresponding angles, etc. Students will use their Geometry textbooks to find the definitions of each vocabulary term, define it, draw and picture, and write any relationship between the pairs of angles. After students have completed the vocab guide, they should look at their diagram and identify which angles are corresponding, alternate interior angles, same side interior angles, etc. (This can be written right on the diagram). Students may use colored pencils to color the angles--like the Geogebratube app if it helps them compare angles. multiple ways.

This may need to be finished during the next class period.

IV. Closure:

5 min

Before students leave, summarize what the students have investigated. They defined types of

angles formed from parallel lines and a transversal. They also discovered the relationships

between each of these angle pairs. Remind students to hold onto their activity worksheet,

vocab guide, and diagram (have them put it into their notebooks).

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