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Common Core For Geometry
Student Outcomes
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)
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