# High School Geometry Worksheets

What is geometry used for in the real world?
One of the very important aspects of mathematics, Geometry is derived from the Greek words which mean Earth’s measurements. Why? Because on the whole, it is concerned with the properties of space and figures. So geometry consists of a lot of lines and shapes, and it helps to find the lengths, volumes, and areas of various shapes.
So how is geometry used in the real world? Let’s take a look.
**Technology** - Geometry comes in handy in various applied fields such as robotics, computers, and video games.
**Architecture** - One of the best examples in the architectural field is the staircases that are built in our homes. They are built on 90 degrees angles. Just like that, geometry is used in the engineering of various buildings with different structures and heights.
**Astronomy** - One of the major uses of geometry is in mapping the positions of stars and planets and the movements of various celestial bodies.
**Art** - Geometry is quite useful when it comes to art. Using lines and angles to perfect figures, symmetry, and much more requires the use of geometry.
**Geographic Information Systems** - Geometry is also a very useful tool when it comes to calculating the positions of GPS, which is measured through latitudes and longitudes. When people ask me my thoughts of geometry I always say, "It's the most useful math in the world!" If you use this type of math on a daily basis, as a grown-up, you must have a very accomplished career. Geometry under most curriculums is a nice mix of relevant real-world applications with a sprinkle of algebra and elementary trigonometry. Don't forget **Geometry Math Posters** make great visuals for your classroom. The topics below are filled with geometry worksheets and lessons that are will help prepare your students.

### Congruence

- Basic Geometry Definitions (HSG-CO.A.1) - Students learn the ground floor of geometric shapes and movements.
- Parallel and Perpendicular Lines (HSG-CO.A.1) - If a pair of lines are known to be parallel it helps us find angles and measures that bisect them both. If lines are perpendicular to one another it gives us a solid right angle to work off of.
- Geometric Transformations within a Plane (HSG-CO.A.2) - We look at transformations that can be tracked easier through the use of the coordinate plane.
- Graphing Complex Transformations (HSG-CO.A.4) - These are geometric movements that can’t be summed up that easy.
- Rotations, Reflections, and Translations of Geometric Shapes (HSG-CO.A.4) - We look at spinning, mirror images, and basic movements of shapes.
- Drawing Transformed Figures (HSG-CO.A.5) - Given a specific set of directions students will create new figures.
- Rigid Motions to Transform Figures (HSG-CO.B.6) - A rigid motion, when referring to figures, is when all the points in a figure are moved.
- Rigid Motions and Congruent Triangles (HSG-CO.B.7) - The focus here is on our three-sided friends.
- Proving Triangle Congruence (HSG-CO.B.8) - This leads us into proof writing territory.
- Geometric Proofs On Lines and Angles (HSG-CO.C.9) - We look at a wide variety of theorems that you can use to write and create proofs.
- Lines and Angles Formed by Transversals (HSG-CO.C.9) - In most cases transversals are only helpful if the pas through parallel lines or form a perpendicular.
- Triangle Proofs (HSG-CO.C.10) - In most cases we are working to prove congruency, but not always.
- Proving Theorems of Parallelograms (HSG-CO.C.11) - There are really four different tendencies we focus on here.
- Making Bisectors of Angles and Lines (HSG-CO.D.12) - We learn how to cut an object or line into two equal parts with bisectors.
- Making Perpendicular and Parallel Lines (SG-CO.D.12) - You will learn how to do this physically and in theory as well.
- Inscribing Shapes in Circles (HSG-CO.D.13) - Students are a little blown away by this concept, when they first see. It can be a little intimidating.
- Dilations and Parallel Lines (HSG-SRT.A.1a) - We look at how the use of parallel lines can help us better understand the nature of a dilation.
- Dilations and Scale Factors (HSG-SRT.A.1b) - Students explore expansions and compressions.
- Similarity Transformations (HSG-SRT.A.2) - Students explore various types of transformations on similar figures.
- Angle Sum and Difference, Double Angle and Half Angle Formulas (HSG-SRT.A.2) - We explore how to use known measures in a triangle to your advantage.
- Corresponding Angles of Similar of Triangles (HSG-SRT.A.3) - Students learn how identify and use corresponding angles to their advantage.
- Proving Triangle Theorems (HSG-SRT.B.4) - There are four main theorems that we key in on here.
- Congruent Triangles: SSS and SAS Theorems (HSG-SRT.B.5) - This is an extensive look at the side-side-side and side-angle-side triangle theorems.
- Congruent Triangles: ASA and AAS Theorems (HSG-SRT.B.5) - We expand to using the angle-side-angle and angle-angle-side theorems
- Triangles (Similarity and Congruence) (HSG-SRT.C.6) - Students get comfortable with the differences and uses of these two traits of triangles.
- Tangent Ratios (HSG-SRT.C.6) - Students learn how to use this nifty little tool to find missing side lengths of triangles.
- Cos and Sin Trigonometric Ratios (HSG-SRT.C.7) - Students learn how to use these ratios to better understand triangles.
- Trigonometric Ratios and the Pythagorean Theorem (HSG-SRT.C.8) - We explore how you can use these tools to learn all about the measures of right triangles.
- Working with Right Triangles (HSG-SRT.C.8) - This is where we spend more time on math application.
- Proving the Formula A = 1/2 ab sin(C) (HSG-SRT.D.9) - We learn how to write a well-developed proof.
- Area of Triangle Using Trigonometry (HSG-SRT.D.9) - We look at how to apply what we have learned to a wide array of situations.
- Using Sine and Cosine (HSG-SRT.D.10) - This section can be used for further review.
- Law of Cosines (HSG-SRT.D.10) - This is helpful when we know the measures of either two sides and an angle that exist between them or if we know all three sides of a triangle.
- Graphs Dealing with Sine and Cosine Problems (HSG-SRT.D.10) - This shows students how to work in graph-based environment.
- Application of the Standard Law of Sines (HSG-SRT.D.10) - This has many applications in physics.
- Law of Sines and the Ambiguous Case (HSG-SRT.D.10) - This is for those not-so common situations.
- Find the Missing Angle Using Trigonometry (HSG-SRT.D.11) - We pull together all that we have learned in this section.
- Similarity of Circles (HSG-C.A.1) - All circles are similar they just scale differently.
- Circles: Inscribed Angles, Arcs and Chords (HSG-C.A.2) - Students learn how to find the measures of all these circle based values.
- Graphs Dealing with Tangent, Cotangent, Secant, Cosecant Problems (HSG-C.A.2) - These are very practical applications of these trig. functions.
- Perimeter of Polygons with Inscribed Circles (HSG-C.A.3) - This can be overwhelming for students, at first. Take this topic slowly with students.
- Angles in Inscribed Right Triangles and Quadrilaterals (HSG-C.A.3) - Learn how to find all the measures involved in these.
- Constructing and Using Tangent Lines (HSG-C.A.4) - Learn how to touch a function at only one point.
- Measurements of Arcs (HSG-C.B.5) - Learn to calculate these missing values.
- Area of Sectors of A Circle (HSG-C.B.5) - We used this in college to figure out who got the biggest and smallest slice of pizza.
- Arc Length and Radian Measure (HSG-C.B.5) - Learn how to find the degree measure of an arc.
- Finding the Equation of Circles (HSG-GPE.A.1) - Learn how to compose these equations on your own.
- Finding the Equation of a Parabola (HSG-GPE.A.2) - Finding the equation of these Us.
- Equations of Ellipses (HSG-GPE.A.3) - My professors called these Egg equations.
- Equations of Hyperbolas (HSG-GPE.A.3) - These are often used in out of this world science to calculate the trajectories of space particles.
- Using Coordinates To Prove Theorems (HSG-GPE.B.4) - A very accurate way of doing this.
- Slopes of Parallel and Perpendicular Lines (HSG-GPE.B.5) - If you know the slope of one parallel line the other one has to be the same. Perpendicular lines, on the other hand are negative reciprocals of one another.
- Finding Midpoints of Line Segments (SG-GPE.B.6) - In most cases a divisor by two will find this for you, if you know the measure of a line.
- Area and Perimeter in the Coordinate Plane (HSG-GPE.B.7) - The coordinates are used to find the measures of the lines, in this case.
- Similar Polygons: Ratio of Perimeters & Areas (HSG-GPE.B.7) - We go through all the different methods that you can use to determine this.
- Finding the Length of Line Segments (HSG-GPE.B.7) - This is related to scale factors.
- Using the Distance Formula (HSG-GPE.B.7) - Use this to find the distance between two points.
- Cavalieri's Principle (HSG-GMD.A.1) - This is often used to calculate the of odd shaped objects.
- Volume of Cylinders and Triangular Prisms (HSG-GMD.A.3) - The same relative is used regardless of which form the shape takes.
- Volume of Cones and Spheres (HSG-GMD.A.3) - This is used extensive in marine science.
- Cross-sections of Three-dimensional Objects (HSG-GMD.B.4) - This has huge application in the field of biology.
- Using Shapes and Measures to Describe Objects (HSG-MG.A.1) - When you have large objects, you can break them down into primitive shapes to learn more about them.
- Using Density in Real-life Situations (HSG-MG.A.2) - These are critical measures that scientists make daily.
- Using Geometry in Design Problems (HSG-MG.A.3) - Architects and engineers make careers off of mastery this form of math.
- Complete the Truth Table (HSG-MG.A.3) - These help you breakdown and understand the validity of compound statements.
- Conditionals Using Logic Tables (HSG-MG.A.3) - These are used to evaluate if-then statements.
- Conjunctions Using Logic Tables (HSG-MG.A.3) - These help evaluate "and" statements.
- Disjunction, Conditionals and Biconditionals (HSG-MG.A.3) - We bring each of these statements to light for you.
- Disjunction Based Logic Tables (HSG-MG.A.3) - This needed more review. A few teachers asked us to build out this topic more, so we did.
- Negation and Conjunction In Logic Statements (HSG-MG.A.3) - These two can be quite confusing and we recommend students read through each problem at least twice.
- Related Conditional: converse, inverse, contra- positive- (HSG-MG.A.3) - Converses are the if-then statements. Inverses are the if not-then not statements. Contrapositives are statements that interchange the hypothesis and the conclusion.
- Truth Values of Compound Sentences (HSG-MG.A.3) - Students learn how to evaluate compound statements.
- Logic : Conjunctions, Disjunctions, and Biconditionals (HSG-MG.A.3) - Biconditionals give students the most trouble, in my experience.
- Truth Value of Open Sentences (HSG-MG.A.3) - This is when we are not sure if a sentence is true or false.
- Using Venn Diagrams Problems (High School Modeling) - This is a powerful form of modelling a math sentence or compound sentence.

### Similarity, Right Triangles, & Trigonometry

### Circles

### Expressing Geometric Properties with Equations

### Geometric Measurement & Dimension

### Modeling with Geometry

### Strategies to Use When Approaching Geometry Worksheets

Geometry problems are different from other math topics you have studied because they require to fully understand what is being asked of you. You may have skipped or skimmed through directions in past topics. That will not work here. Always start these types of problems by developing a game plan. Take your time to determine what is being given to you and what they are looking for in a solution. The given information is almost always what you will be using to find a missing measure. Whenever possible, fill in the diagrams by displaying what side, angle, segment, or piece should be focused on. If a diagram is not provided for you draw one up. Then decide how the givens relate to your unknown value. Always focus on congruence of triangles, this will tell you a lot about any missing side. When you can identify an isosceles triangle, you can always use if the if sides then angle technique. The same can be said about if angle then sides method. Parallel lines are great helps proving angle measures, so always identify them. Once you put together a solution, reverse engineer it and work backwards to see if it proves the givens. Getting good at this topic requires a great deal of patience and repetition. Make sure to approach it that way in your mind.