UGA Trio UB/UBMS Geometry 6-23-2025
On this page:
Homework Problems on Transversals
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Find all the missing angle measurements in the following WITHOUT A PROTRACTOR:
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[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
In the diagram below, $m \parallel n$, and the angles are as marked. Find $x$.
[/bluebox]
[hint] Draw a line parallel to both $m$ and $n$ that passes through $A$. [/hint]
[solution] $75^\circ$ [/solution]
Homework Problems on Triangles
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Two angles in a triangle have measures $30^\circ$ and $57^\circ$. What is the measure of the third angle? [/bluebox]
[solution] $93^\circ$ [/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Find $\angle ZYP$ in the diagram below WITHOUT USING A PROTRACTOR.
[/bluebox]
[solution] $41^\circ$ [/solution]
Project
A significant portion of your grade is built into completing a course project. If you work in a group, you will be required to submit peer evaluations as part of your progress reports. Late progress reports will have points deducted.
- Sign-up form: https://forms.gle/pugDSZCoMoqZ6AbR8
Timeline:
- Progress report (15% of project grade): Due June 27th.
- Progress report (15% of project grade): Due July 2nd.
- Project (70% of project grade): Due July 4th.
The following projects are available:
[bluebox] [bluetitle]Project 1 (Truss using Craft Sticks).[/bluetitle]
Description: Students will design and build a truss bridge using craft sticks and glue. Their designs must incorporate at least two types of triangles (isosceles, scalene, equilateral) and demonstrate how triangles create structural strength. Must be done in a group of 3 or 4 students. [/bluebox]
[bluebox] [bluetitle]Project 2 (Mandalas).[/bluetitle]
Description: Students will design geometric mandalas based on tutorials like https://youtu.be/48A1lwqfCZQ. Using compass, straightedge, and protractor techniques, students will divide circles evenly into sectors and incorporate repeating motifs. Final designs will include labeled angle measures and symmetry notes. This can be a one-student project but may be done in groups. [/bluebox]
[bluebox] [bluetitle]Project 3 (Origami constructions).[/bluetitle]
Description: Use origami (paper folding) to construct and measure geometric angles and lines without using a compass or protractor. Students will explore how folds can be used as a geometric tool to bisect angles, create perpendicular lines, and trisect angles with paper instead of tools using websites like https://www.britishorigami.org/cp-resource/folding-angles/. This can be a one-student project but may be done in groups. [/bluebox]
[bluebox] [bluetitle]Project 4 (Geometric constructions).[/bluetitle]
Description: Students will complete a series of classical Euclidean compass-and-straightedge constructions, including angle bisectors, perpendicular bisectors, perpendicular lines, circles through 3 points, and parallel lines. Students will annotate diagrams with explanations of the geometric logic behind each construction. This can be either a one-student project or can be done in groups. [/bluebox]
[bluebox] [bluetitle]Project 5 (Solve Some Problems).[/bluetitle]
Description: Students will be given a few involved problems related to topics in the course, solve them, and produce a formal write-up detailing the solution. This can be done either individually or as a group project. [/bluebox]