Exploring Triangles



Exploring Triangles

Reporting categories Measurement, Geometry

Overview Students explore and identify characteristics of triangles and types of triangles while also discovering that the sum of the angles of a triangle total 180º.

Related Standards of Learning 6.13, 6.14

Objectives

• The student will measure right, obtuse, and acute triangles.

• The student will identify the sum of the measures of the angles of any triangle.

• The student will determine that the sum of the measures of the angles of a triangle is 180º.

Materials needed

• “Exploring Triangles” (two pages), one copy for each student

• Protractors

Instructional activity

1. Review the definitions of acute, obtuse, and right angles.

2. Draw an acute triangle on the board or overhead. Label the measure of each of the interior angles. Ask students to name the shape (triangle) and to describe its characteristics (3 sides, 3 angles).

3. Draw an obtuse triangle on the board or overhead, with the angle measures labeled. Instruct students to compare and contrast the 2 triangles. Allow students to share their ideas.

4. Draw a right triangle on the board or overhead, with the angle measures labeled. Instruct students to compare and contrast with the other 2 triangles. Allow students to share their ideas.

5. Explain to students that one way to classify triangles is by their angles. Have students use prior knowledge of angle types to predict the name of each triangle based on their angle measures. Allow students to share their ideas in naming. Ensure that all students properly named each triangle as acute, right, or obtuse. Lead students to realize that triangles are named based on the size of their largest angle.

6. Distribute “Exploring Triangles” worksheet to students and have them complete (it may be necessary to review proper procedure for measuring angles prior to assigning this worksheet). You may find it helpful to complete the first problem with students. Check student responses on worksheet.

7. Draw two triangles (one acute, one obtuse) on the board or overhead with the measure of the interior angles labeled. Ask students to identify the type of each triangle.

8. Instruct students to make a list of the similarities of the triangles. Have students share what they found. Lead students to realize that the sum of the angles in both triangles is 180º.

9. Ask students to predict if all triangles’ interior angles will have a sum of 180º and to justify their predictions. Ask students if they know a way to find out if their predictions are correct or incorrect (check more examples).

10. Refer students to the “Exploring Triangles” worksheet they just completed. Have students check their theory by finding the sum of the measures of the angles in each triangle. Instruct students to record findings in a chart. Work additional examples if necessary.

11. Have students write an explanation of what they discovered, and allow students to share their ideas. Ensure that all students understand that the sum of the measures of the interior angles of a triangle totals 180º.

Sample assessment

• Informally assess as students work to complete activity.

• Follow up with an additional independent activity that requires students to find a missing angle measure when two of the angles are given.

Follow-up/extension

• Have the students complete the activity, “Sum Angles of a Triangle,” which is found at

Sample resources

Learning and Teaching Measurement: 2003 Yearbook with Classroom Activities Companion Booklet, NCTM, 2003. Information related to measurement and activities that go beyond the content.

– VDOE mathematics module, “Geometry for Middle School Teachers,” lesson title: “Sum Angles of a Triangle.”

– Ideas and resources for teaching measurement that includes lesson plans, materials, common questions, and software.

– Information on measurement from Principles and Standards for School Mathematics.

lesson/math/geometry/circlesingeo.html – Activities to introduce the concept of circumference.

Exploring Triangles

Name: Date:

Record triangle findings in the chart below.

|Triangle |Measure (1 |Measure (2 |Measure (3 |Sum |

|1 | | | | |

|2 | | | | |

|3 | | | | |

|4 | | | | |

|5 | | | | |

|6 | | | | |

| | | | | |

| | | | | |

| | | | | |

Exploring Triangles

Name: Date:

Use a protractor to measure all interior angles of each triangle. Label the measure of each angle. Determine the type of triangle based on the angle measures.

1. 2.

Type _______________ Type _______________

3. 4.

Type _______________ Type _______________

5. 6.

Type _______________ Type _______________

Sample released test items

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