Welcome! The Desmos Geometry Tool is a powerful and interactive workspace that allows you to visualize and explore plane geometry through construction, measurement, transformations, and more! Get started with the tips below, or check out the Geometry User Guide.

## Creating Your First Construction

When you visit the Geometry tool, you’ll see the four main components: the geometry toolbar, graph paper, token navigator, and expression list.

### Geometry Toolbar

The Geometry toolbar is the menu along the top containing all of the available construction tools. You can use these tools to construct points, various types of lines, circles, angles, and polygons. You can also select items with the select tool to edit or transform them.

### Selected Items Menu

When you select a geometric object, the geometry toolbar changes to the Selected Items Menu. This menu allows you to delete, hide, transform, or style the selected object.

Open the transformation menu to translate, reflect, dilate, or rotate your object.

The ‘more options’ button, represented by three dots, opens a style menu that allows you to change the color of your object and move it from the token navigator to a folder in the expression list. For points, segments, and angles there is also an option to label your object which will show the coordinate point, segment length, and angle measure respectively.

### Graph Paper

The graph paper is where constructions take place. You can insert items into this space using the geometry toolbar or the expression list. Items on the graph paper are dynamic. For example, with the select tool, you can click and move draggable points and see how that movement affects the overall construction. You can also pan with the mouse and zoom with the zoom buttons.

### Token Navigator

The token navigator is at the top of the expression list (to the right of the ‘add item’ button). Here, you can see token references for the objects you construct on the graph paper. Hover over hidden tokens to reveal the location of those objects or select tokens to change the object's properties. You can also click and drag a token into the expression list to work with it algebraically, give it a name, or adjust other style settings.

### Expression List

The expression list is the panel on the left side of the screen where you can enter expressions and functions. If you’re familiar with the Desmos Graphing Calculator, you’ll notice this part is the same!

You can see a list of available functions by opening the Desmos keyboard on the bottom left. Functions specific to geometry can be found under the headings ‘geometry tools,’ ‘properties & measurements,’ and ‘transformations.’ In the Geometry User Guide, you will find a list of available functions, the arguments they take, and an example of each. Geometry functions can be typed into the expression list and then receive inputs by selecting items on the graph paper.

For example, let’s use the expression list to find the intersection of two circles. We can find one intersection by typing intersection() directly into the expression list, or by finding the intersection function from the keypad menu. To see both intersections, reverse the order you click on the circles.

While many geometric functions and commands allow you to click on an object in the graph to insert it into an expression, this feature is sometimes restricted to prevent accidental inputs. However, you can insert a token wherever you’d like. To do so, place your cursor in the desired position of the expression list, then hold down shift and click on the geometry object you want to insert.

For example, the rotation function \(R(x)\) rotates an object \(x\) around the origin by \(90\) degrees. To use this rotation function, first click to place your cursor inside of the parentheses of \(R( )\), then hold shift and click on the polygon in the graph space. Give this a try by clicking on the image to open the graph.

## Save and Share Your Construction

You can save your constructions to view and edit them later by clicking the blue ‘save’ button on the top left next to the construction title. If you press the save button while signed out, you will be prompted to sign in or create an account. You can also access all of your previously saved constructions by clicking the hamburger button on the top left.

Share your construction by clicking on the ‘share graph’ button in the top right corner next to your account name. Use this menu to copy your construction’s unique link. You can send this link to anyone, and they’ll be able to see your construction.

## Learn More

- Desmos Geometry User Guide
- Geometry Keyboard Shortcuts
- Connections Between Geometry and Algebra
- Labels
- Polygons
- Transformations

Please write in with any questions or feedback to support@desmos.com.