Related Topics:

Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Student Outcomes

- Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is two-thirds of the way along each median from the intersected vertex.
- Using coordinates, students prove the diagonals of a parallelogram bisect one another and meet at the intersection of the segments joining the midpoints of opposite sides.

**Analytic Proofs of Theorems Previously Proved by Synthetic Means**

Classwork

**Exercises**

Let π΄(30,40), π΅(60,50), and πΆ(75,120) be vertices of a triangle.

a. Find the coordinates of the midpoint π of π΄π΅ and the point πΊ1
that is the point one-third of the way along
ππΆ, closer to π than to πΆ.

b. Find the coordinates of the midpoint π of π΅πΆ and the point πΊ2
that is the point one-third of the way along ππ΄,
closer to π than to π΄.

c. Find the coordinates of the midpoint π
of πΆπ΄ and the point πΊ3
that is the point one-third of the way along π
π΅,
closer to π
than to π΅.

**Exercise 1**

a. Given triangle π΄π΅πΆ with vertices π΄(π1, π2), π΅(π1, π2), and πΆ(π1, π2), find the coordinates of the point of
concurrency of the medians.

b. Let π΄(β23, 12), π΅(13, 36), and πΆ(23,β1) be vertices of a triangle. Where will the medians of this triangle
intersect? (Use βTylerβs formulaβ from part (a) to complete this problem.

**Exercise 2**

Prove that the diagonals of a parallelogram bisect each other)

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.