Geometry Topics
Below I have listed the topics you will be learning, the learning objectives or goals for each chapter and the state standards that are associated with each topic. A link to a detailed list of all state math standards can be found at the bottom of the page.
Chapter 1: Tools of Geometry
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 2: Reasoning and Proof
Standard: Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.
In this chapter you will
Chapter 3: Parallel and Perpendicular Lines
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 4: Congruent Triangles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 5: Relationships within Triangles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 6: Polygons and Quadrilaterals
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 7: Similarity
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
Chapter 8: Right Triangles and Trigonometry
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods. In this chapter you will
Chapter 9: Transformations
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
Chapter 10: Area
Standard: Calculate measurements of plane and solid figures; know that physical measurements depend on the choice of a unit and that they are approximations.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
Chapter 11: Surface Area and Volume
Standard: Calculate measurements of plane and solid figures; know that physical measurements depend on the choice of a unit and that they are approximations.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
Chapter 12: Circles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
Chapter 1: Tools of Geometry
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- define basic geometric figures.
- know that point, line and plane are undefined.
- learn postulates about basic geometric concepts.
- be able to measure segments with and without a coordinate grid.
- use the midpoint and distance formula.
- use protractors to measure angles.
Chapter 2: Reasoning and Proof
Standard: Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.
In this chapter you will
- observe patterns leading to making conjectures.
- solve equations giving their reasons for each step and connect this to simple proofs.
- prove geometric relationships using given information, definitions, properties, postulates, and theorems.
Chapter 3: Parallel and Perpendicular Lines
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- use postulates and theorems to explore lines in a plane.
- use coordinate geometry to examine the slopes of parallel and perpendicular lines.
- use Triangle-Angle Sum Theorem
- write equations using slope-intercept form.
- write equations using point-slope form.
Chapter 4: Congruent Triangles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- visualize the triangles placed on top of each other.
- use tick marks and angle marks to label corresponding sides and corresponding angles.
- use the Side-Side-Side Postulate, the Side-Angle-Side Postulate, the Angle-Side-Angle Postulate, the Angle-Angle-Side Theorem, and the Hypotenuse-Leg Theorem.
- use the definitions of triangles and congruent parts to classify triangles.
Chapter 5: Relationships within Triangles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- use the Midpoint Formula to find midsegments of triangles.
- use the Distance Formula to examine relationships in triangles.
- examine inequalities in one and two triangles.
- begin with the negation of the statement to be proved and will show a counterexample.
Chapter 6: Polygons and Quadrilaterals
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- derive the formula for angle measures of a polygon.
- use properties of parallel and perpendicular lines and diagonals to classify quadrilaterals.
- use coordinate geometry to classify special parallelograms.
- examine slope and segment length in the coordinate plane.
- use the Distance Formula in the coordinate plane.
Chapter 7: Similarity
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
In this chapter you will
- form proportions based on known lengths of corresponding sides.
- use the Angle-Angle Similarity Postulate.
- use the Side-Angle-Side Similarity Theorem.
- use the Side-Side-Side Similarity Theorem.
- identify corresponding parts of similar triangles.
Chapter 8: Right Triangles and Trigonometry
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods. In this chapter you will
- use the Pythagorean Theorem
- use concepts of 30-60-90 and 45-45-90 triangles.
- use trigonometric ratios to form proportions.
- examine the sine, cosine and tangent ratios.
- describe vectors using magnitude and direction.
Chapter 9: Transformations
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
- explore translations, reflections, rotations and dilations.
Chapter 10: Area
Standard: Calculate measurements of plane and solid figures; know that physical measurements depend on the choice of a unit and that they are approximations.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
- use formulas to find areas of parallelograms, triangles, trapezoids, rhombuses and kites.
- explore area concepts related to regular polygons.
- use trigonometry to find areas.
- find circumferences and areas of circles.
- examine ratios among similar figures.
- be able to find the area of a figure similar to the original figure.
Chapter 11: Surface Area and Volume
Standard: Calculate measurements of plane and solid figures; know that physical measurements depend on the choice of a unit and that they are approximations.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
- examine cross sections.
- use formulas to find surface areas and volumes of prisms, cylinders, cones, pyramids and spheres.
- examine ratios among similar solids.
- be able to find volume and surface area of a figure similar to the original figure.
Chapter 12: Circles
Standard: Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.
Standard: Solve real-world and mathematical geometric problems using algebraic methods.
In this chapter you will
- examine angles formed by lines that intersect inside and outside a circle.
- relate arcs and angles.
- use properties of tangent lines.
- use relationships among chords, arcs, and central angles.
- solve problems with angles formed by secants and tangents.
- write and use equations of circles.
Algebra 8 Standards
In algebra 8, students learn the standards required by the state. You can click on the link below to view the state standards. Minnesota K-12 Academic Standards in Mathematics (2007)
In algebra 8, students learn the standards required by the state. You can click on the link below to view the state standards. Minnesota K-12 Academic Standards in Mathematics (2007)