Syllabus

Geometry Summer Offering

Week 1: Introduction to Geometry
As students begin the course, this week sets a foundation for the course by presenting expectations, modeling some of the different activities that students will see throughout the course and clarifying communication tools. Virtual introductions will help begin to build a reflective and safe community of learners. This week will also introduce students to the course content by identifying the important terms associated with geometry; this is essential to identify basic geometric figures in order to understand their properties.

This week’s activities will focus on the following objectives:
• Understand the scope of content, requirements, and expectations for the course.
• Identify basic geometric terms
• Identify and name line segments
• Apply the Distance and Midpoint Formulas
• Identify and name angles
• Measure angles
Week 2: Lines, Angles, and Triangles
This week, students will investigate more with lines, angles, and triangles. During this week, they will explore types of angles as well as angles formed by two parallel lines cut by a transversal. They will explore the different relationships of the angles formed and which angles are congruent as well as use their knowledge of these angles to determine missing measurements in various figures. Also, students will begin working with perpendicular lines in addition to parallel lines. Parallel and perpendicular lines should be familiar as students may have seen in their Algebra course. Here, students will explore these lines within the coordinate plane. Finally, they will be introduced to triangles this week. Students will begin by classifying triangles and understanding their different properties.

This week’s activities will focus on the following objectives:

• Find the measure of angles formed by intersecting lines in figures with vertical angles, complementary angles, or supplementary angles
• Identify and show two lines are parallel or perpendicular
• Find the equation of a line through a point that is parallel to a given line
• Find the equation of a line through a point that is perpendicular to a given line
• Classify triangles and identify their properties
Week 3: Congruence and Similarity
This week, students will be introduced to the topic of congruent triangles. They will learn about various congruence theorems that are applied in order to prove that two triangles are congruent. These congruence theorems focus on the relationships between the sides and angles of congruent triangles. They will also apply these theorems in order to find the measures of side lengths and angles of triangles. In addition, students will also explore similarity and how this differs from congruence. Specifically, students will use similar triangles to explore the properties of triangles.

This week’s activities will focus on the following objectives:

• Determine if two triangles are congruent
• Apply the properties of congruent triangles to find angle measures and side lengths
• Apply and prove the ASA, SAS, SSS, AAS, and HL Triangle Congruence Theorems
• Determine the measures of corresponding lengths and corresponding angles in similar figures
• Show triangles are similar using AA, SAS, and SSS Triangle Similarity
Week 4: Quadrilaterals and Other Polygons
This week, students will focus on quadrilaterals as well as other types of polygons. Quadrilaterals are a specific type of polygon; they are specifically 4-sided polygons. Students will explore various types of quadrilaterals such as squares, rectangles, trapezoids, kites, and rhombuses. There are similarities, as well as differences, among these types of quadrilaterals. In addition, students will also review the different types of polygons as well as explore properties of polygons. As they explore various quadrilaterals this week, students will also learn how to determine the area and perimeter of these figures.

This week’s activities will focus on the following objectives:

• Identify parallelograms and the relations between their sides, angles, and diagonals
• Show that quadrilaterals with certain characteristics are parallelograms
• Identify, show, and apply the properties of different types of quadrilaterals
• Find perimeter and area of polygons
Week 5: Trigonometry
During this week, students will be introduced to trigonometry, which is the study of triangles. In trigonometry, triangles are explored in two areas: right triangles and non-right triangles. As students explore right triangles, they will be introduced to trigonometric ratios and how they relate to right triangles. As they explore non-right triangles (acute and obtuse), students will learn how they apply trigonometric functions to determine the measure of side lengths and angles. Specifically, students will learn the Law of Sines and the Law of Cosines to calculate these measures. Finally, they will also determine how to find areas of non-right triangles.

This week’s activities will focus on the following objectives:

• Identify and apply the Pythagorean Theorem
• Identify and apply the trigonometric rations for the acute angles of a right triangle
• Identify and apply the inverse trigonometric ratios for the acute angles of a right triangle
• Calculate side lengths and angle measures in right triangles
• Use the Law of Sines to find side lengths and angle measures of non-right triangles
• Use the Law of Cosines to find side lengths and angle measures of non-right triangles
Week 6: Transformations and Symmetry
This week, students will focus their attention on various types of transformations. They will explore translations, reflections, and rotations as well as identifying different types of symmetry. Throughout the week, students will take a visual approach to explore these transformations on the coordinate plane. They will construct their own transformations using what they will learn this week.

This week’s activities will focus on the following objectives:

• Identify the coordinates of the vertices of an image
• Identify translations, reflections, and rotations
• Draw the image of figures using translations, reflections, or rotations
Week 7: Circles
During this week, students will focus on the properties of circles. Specifically, they will learn about different types of angles and segments related to circles and calculate their measures as well as learn about different properties. Students will apply these properties to determine side lengths and angle measures. In addition, they will also use these properties to solve various application problems. Finally, students will explore the circumference and the area of a circle and calculate these within application problems.

This week’s activities will focus on the following objectives:

• Determine the measures of central angles
• Determine the measures of inscribed angles of circles
• Identify and measure tangent lines to circles
• Identify relationships between the segment lengths formed by line segments that intersect a circle
• Identify the relationships between the angles formed by lines that intersect a circle
Week 8: Three-Dimensional Figures
This is the final week of the course. During this week, students will focus their attention on three-dimensional figures. Specifically, they will explore volume as well as surface area. They will learn the different formulas for volume and surface area for each three-dimensional figure. Students will also learn how to apply these formulas to calculate volume and surface area in various applications. Finally, at the end of the week, students will take their final exam.

This week’s activities will focus on the following objectives:

• Compare formulas for area and formulas for volume
• Apply formulas and calculate the volume of cylinders, pyramids, cones, and spheres
• Apply formulas and calculate the surface area of cylinders, pyramids, cones, and spheres