Geometry, Semester A

Course Description

Geometry A is the first semester in a two-semester series that explores the study of points, lines, planes, 2D shapes, and 3D solids. Students will form logical arguments, construct two-column proofs, and support their reasoning through theorems and postulates discovered over two thousand years ago. In Geometry A, students will learn to use both ancient tools (like a compass and straight edge) and modern technologies (like graphing utilities and videos) to develop skills that are used daily by carpenters, lawyers, and artists. Students will gain a new perspective about the world around them, including why bees use hexagons to build their hives, how to form logical arguments that will be irrefutable, and how to create visually appealing artwork through geometry. As part of this course, students are expected to create models, including floor plans, and compass, straightedge, and protractor constructions.  

Texas Essential Knowledge and Skills (TEKS) 

UTHS courses are designed in alignment to the Texas Essential Knowledge and Skills (TEKS) which define the skills and content to be taught in each course and grade level in the state of Texas.

Semester Topics

• Unit 1: Building Blocks of Geometry
• Unit 2: Reasoning and Proofs
• Unit 3: Transformations
• Unit 4: Triangles and Constructions

Course Objectives

Upon completing this course, you will be able to—

• contrast Euclidean and spherical geometries through examining the concepts of points, lines, planes, parallel lines, and the sum of the angles in a triangle; 
• transform figures in a plane by dilating, translating, reflecting, and rotating;  
• describe a transformation in words and in coordinate notation; 
• determine the validity of a conditional statement; and if it is false, give a reasonable counterexample;  
• identify, compare, and contrast a conditional statement with its converse, inverse, and contrapositive; 
• prove various theorems about angles and apply these theorems to solve problems;  
• prove triangles are congruent using triangle congruence theorems; 
• verify theorems about triangles, such as the Pythagorean Theorem, and apply these theorems to solve problems. 

Required Course Materials

Please visit the Computer Requirements page to view minimum device, internet, and application requirements for all UT High School courses. Generally, a desktop or laptop device five (5) years or newer with access to an office suite, such as Microsoft Office or Google Workspace, will be adequate to participate in most UTHS courses. 

Unless otherwise noted, students are responsible for purchasing or securing all the following course materials:

• Textbook: A textbook is not required for this course.
• Interactive Notebook: A paper or digital composition book is acceptable. For paper composition books, please also have the following items on hand:  
  • Pens or Pencils
  • Tape or Glue
• Graphing Calculator: A TI-84 is recommended for all UTHS math courses. Please review the UTHS Graphing Calculator Policy before purchasing a device.
• Miscellaneous Items:
  • Compass
  • Straight Edge
  • Protractor

Course Organization

Students must complete the course in sequence: You will not be able to access the next unit until all work in the preceding unit is completed. You may take your final exam only after completing all units and submitting all graded assignments.  

• Units: Each unit includes multiple lessons and graded assignments as well as ungraded practice quizzes to help you check your understanding of the material.
  
  
• Summative Assessments: Each course includes two online, virtually proctored summative assessments testing your understanding of the material presented in the preceding 2-3 Units.
  • Format: Online, Multiple-choice
  • Time Allowed: 1 hr 30 min
    
    
• Final Exam: Each course includes an online, virtually proctored final exam testing your knowledge of all material presented in the course.
  • Format: Online, Multiple-choice
  • Time Allowed: 3 hrs 20 min

Course Grade Weighting

Your final course grade is calculated by weighting the three assignment groups displayed in the table below:

Online Proctored Exams

All course exams, including both summative assessments and the final exam, must be completed online. Students must test online with Proctorio and are required to add the Proctorio extension to either their Microsoft Edge or Google Chrome browser—installation instructions are provided in the student's course. Proctorio uses a student's computer, web camera, and microphone to record video of both the student and their desktop during the exam. Then, UTHS instructors review the student's exam video data collected by Proctorio. Only authorized UTHS staff and instructors can view the exam recordings. Student data is not shared with any persons or organizations outside of UTHS and are deleted after one year. We encourage you to visit Proctorio's Data Security and Privacy site pages to learn more about how we protect student date.