Standard 5: Make formal geometric constructions with a variety of tools and methods.

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General Information

Number: MA.912.GR.5

Title: Make formal geometric constructions with a variety of tools and methods.

Type: Standard

Subject: Mathematics (B.E.S.T.)

Grade: 912

Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.GR.5.AP.1

Construct a copy of a segment.

MA.912.GR.5.AP.2

Construct the bisector of a segment, including the perpendicular bisector of a line segment.

MA.912.GR.5.AP.3

Select the inscribed and circumscribed circles of a triangle.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

Using a Compass To Construct a Tangent Line:

Students are asked to construct a tangent line to a given circle from a given exterior point.

Type: Formative Assessment

Constructing a Congruent Angle:

Students are asked to construct an angle congruent to a given angle.

Type: Formative Assessment

The Sprinters’ Race:

Students are given a grid with three points (vertices of a right triangle) representing the starting locations of three sprinters in a race and are asked to determine the center of the finish circle, which is equidistant from each sprinter.

Type: Formative Assessment

Constructing a Tangent Line:

Students are asked to complete and justify the construction of a line tangent to a circle from an exterior point.

Type: Formative Assessment

Constructing a Congruent Segment:

Students are asked to construct a line segment congruent to a given line segment.

Type: Formative Assessment

Regular Hexagon in a Circle:

Students are asked to construct a regular hexagon inscribed in a circle.

Type: Formative Assessment

Equilateral Triangle in a Circle:

Students are asked to construct an equilateral triangle inscribed in a circle.

Type: Formative Assessment

Construct the Center of a Circle:

Students are asked to construct the center of a circle.

Type: Formative Assessment

Square in a Circle:

Students are asked to construct a square inscribed in a circle.

Type: Formative Assessment

Bisecting a Segment and an Angle :

Students are asked to construct the bisectors of a given segment and a given angle and to justify one of the steps in each construction.

Type: Formative Assessment

Inscribed Circle Construction:

Students are asked to use a compass and straightedge to construct an inscribed circle of an acute scalene triangle.

Type: Formative Assessment

Circumscribed Circle Construction:

Students are asked to use a compass and straightedge to construct a circumscribed circle of an acute scalene triangle.

Type: Formative Assessment

Constructions for Perpendicular Lines:

Students are asked to construct a line perpendicular to given line (1) through a point not on the line and (2) through a point on the line.

Type: Formative Assessment

Lesson Plans

Keeping Triangles in Balance: Discovering Triangle Centroid is Concurrent Medians:

In this lesson, students identify, analyze, and understand the Triangle Centroid Theorem. Students discover that the centroid is the point of concurrency for the medians of a triangle and recognize its associated usage with the center of gravity or barycenter. This set of instructional materials provides the teacher with hands-on activities using technology as well as paper-and-pencil methods.

Type: Lesson Plan

What's the Point? Part 2:

In this lesson, students use a paper-folding technique to discover the properties of angle bisectors. At the conclusion of the activity, students will be able to compare/contrast the points of concurrency of perpendicular and angle bisectors.

Type: Lesson Plan

Circumnavigating the Circumcenter:

Students use the concurrent point of perpendicular bisectors of triangle sides to determine the circumcenter of three points. Students will reason that the circumcenter of the vertices of a polygon is the optimal location for placement of a facility to service all of the needs of sites at the vertices forming the polygon.

Type: Lesson Plan

Right turn, Clyde!:

Students will develop their knowledge of perpendicular bisectors & point of concurrency of a triangle, as well as construct perpendicular bisectors through real world problem solving with a map.

Type: Lesson Plan

Halfway to the Middle!:

Students will develop their knowledge of mid-segments of a triangle, construct and provide lengths of mid-segments.

Type: Lesson Plan

Location, Location, Location, Location?:

Students will use their knowledge of graphing concurrent segments in triangles to locate and identify which points of concurrency are associated by location with cities and counties within the Texas Triangle Mega-region.

Type: Lesson Plan

St. Pi Day construction with a compass & ruler:

St. Pi Day construction with compass

This activity uses a compass and straight-edge(ruler) to construct a design. The design is then used to complete a worksheet involving perimeter, circumference, area and dimensional changes which affect the scale factor ratio.

Type: Lesson Plan

What's the Point? Part 1:

This is a patty paper-folding activity where students measure and discover the properties of the point of concurrency of the perpendicular bisectors of the sides of a triangle.

Type: Lesson Plan

Original Student Tutorials

Angle UP: Player 1:

Explore the construction processes for constructing an angle bisector, copying an angle and constructing a line parallel to a given line through a point not on the line using a variety of tools in this interactive, retro video game-themed tutorial.

NOTE: This tutorial uses both the angle bisector construction and the construction to copy an angle as an extension opportunity to also construct a line parallel to a given line through a point not on the line. Students also learn to identify corresponding angles created when a transversal crosses parallel lines, and discover using Geogebra that these angles are congruent.