 Geometry Computer Labs

by

Vicki Tarleton

Research shows that students will retain information better if they learn through various constructive, interesting, and engaging means. Geometer's Sketchpad is a wonderful technological tool that can make the discovery of common geometry definitions, theorems, postulates, etc. a richer learning experience than a traditional lecture approach.

The following geometry labs are designed so that your students can explore, investigate, discover, make conjectures, and learn new concepts through the use of technology. These labs are not set up in a sequential fashion so that they may be accessed as needed. Students should have a basic introduction and understanding of Geometer's Sketchpad before being assigned any of these lessons.

Segments and Angles

This lab is an exploration to discover the sum of the angles of a triangle, of a quadrilateral, and of a pentagon. In addition, students will learn about the midpoint, angle bisector, and the segment addition postulate.

This is a nice lab in that students look at angle pairs on GSP, make their own conclusions, and then define the angle pairs. The angle pairs explored are adjacent, vertical, linear pairs, supplementary, and complementary angles.

Parallel lines and the special angle pairs (alternate interior and exterior, consecutive interior, and corresponding) made by a transversal are explored in this lab. The relationship between the pairs of angles and their measures can be discovered.

This lab is an exploration to discover how the lengths of the sides of a triangle relate to the angle measures. Discoveries about acute, obtuse, right, equiangular, equilateral, scalene, and isosceles triangles are also to be made. In addition, a triangle's exterior and remote interior angles and properties can be investigated.

Students have the opportunity to define and discover the properties of altitudes, medians, perpendicular bisectors, and angle bisectors of triangles. In particular, they are looking at the circumcenter, incenter, and centroid for triangles and what happens with these in acute, obtuse, and right triangles.

Special Right Triangle Relationships

In this lab, students are prompted to make discoveries about 30-60-90 and 45-45-90 triangles. Students should be able to discover the ratios of the legs and the ratios of the legs and hypotenuse.

This lab allows the students see a visual representation of congruent triangles. In addition, students will see how the congruency postulates hold for congruent triangles.

Even though this can be experienced as a lab in the classroom using protractors, this is a good basic use of sketchpad to improve computer skills and provide the use of technology. Students should be able to see a pattern for the sum of interior angles and exterior angles of convex polygons by looking at a triangle, quadrilateral, pentagon, and hexagon on the computer.

This computer lab will help guide students to learn the 5 characteristics of a parallelogram.

This is a computer lab which allows for the discovery of the properties of the 3 polygons named. Students should have the basic knowledge of parallelograms and know their characteristics prior to completing the lab.

This lab is deigned to help students investigate and discover properties of tangent lines to circles. In addition, students will also explore angle measures when chords intersect in the interior of the circle, when two secants intersect in the exterior of the circle, and when a secant and a tangent intersect in the exterior of the circle.

Chords and Secant Relationships

This lab is an exploration of chords, tangents, and secants of a circle. Students can discover the relationship of the measures of the lengths respective to the above segments of a circle.

Arcs, Chords, and Inscribed Angles of Circles

The first part of this lab is an exploration to discover the relationship of a diameter that is perpendicular to a chord. The second part of the lab has the students discover when two chords of a circle have congruent lengths. The final part of the lab shows the relationship between an inscribed polygon of a circle and the angle measures.

Heron's Formula

In this lab, students will construct triangles and find their area. Then using the lengths of the sides of the triangle, they will discover how the area can be found. In the end, Heron's formula is developed.

Chinese Tangram

This is a lab to help students set up tangrams by using the computer. The relationship of the area of the polygons are also explored.

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