need help with attached due tonight at 10 pm

Conceptual Project

Important: Save your work and responses to the project in a document on your computer. Save the document as FirstName_LastName_EulerLine_Project. You will be required to submit the saved project as part of the assessment for this lesson!

An Euler line is a line segment that passes through a triangle's centroid, circumcenter, and orthocenter. These points of concurrency and are located using the following constructions:

• Centroid: point of concurrency of the three medians of the triangle. A median is the line from a vertex of the triangle to the midpoint of the opposite side.

• Circumcenter: point of concurrency of the three perpendicular bisectors of the triangle’s three sides.

• What three points of concurrency always lie on a line?

• What is the ratio of the length of segment DE to segment EF?

• What point of concurrency divides the Euler segment into two parts?

• Orthocenter: point of concurrency of the three altitudes of the triangles sides. An altitude is a perpendicular line from a vertex to the opposite side.

For this project, you will be constructing the Euler's line of a triangle. For this project, you will be constructing the Euler's line of a triangle. There are only two acceptable methods for this construction: by hand (using a compass and straightedge) OR by using the online tools at Geogebra. Please note that any drawings done in a word processing document, Google doc, or even a hand sketch (meaning, not using a compass and straightedge) will NOT be accepted. If you submit anything but a hand-drawn construction or a Geogebra file your project will not be graded and you will have to re-submit your project.

If doing your construction by hand, make sure that your construction marks are visible. Mark any 90° angles on your construction, as well as marking any congruent segments (for example, when drawing a median make sure you mark the two segments created as congruent). It is a good idea to practice the constructions before you work on your conceptual project. If you are using Geogebra, you must include your steps. To do this, go to the settings menu and in the ‘basic’ submenu click on ‘show’ under the words Navigation Bar for Construction Steps. Close the settings menu and in the lower right corner will be a button to show your construction protocol. Be careful it sometimes hides behind the ‘show full screen’ button. Hover over the area until ‘construction protocol’ shows up. Copy and paste all your steps into a word document and attach with your construction. Please make sure you have your name and ‘construction protocol’ in the file name. You may have to scroll down to get all of your steps.

Materials:

• Compass

• Triangle (provided below)

• Straightedge or ruler

triangle 

Steps:

Using the given triangle ABC,

• Construct the circumcenter and label this as point D.

• Construct the centroid and label this as point E.

• Construct the orthocenter and label this as point F.

• Using a straightedge, draw the line that connects points D, E, and F.

• Using a ruler, measure the distance between points D and E and the distance between points E and F.

After completing your construction, answer the following questions. Your responses should be part of the file you upload for your teacher to grade.