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Concurrency of the Medians of a Triangle
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Concurrency of the Medians of a Triangle as shown in Geogebra
Statements Reasons
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Triangle ABC, D and E are midpoints, Given/ these constructions
BD and CE are medians
---------------------------------------------------------------------------------------------------------------------
Intersect G using intersection tool Intersecting Lines Postulate
---------------------------------------------------------------------------------------------------------------------
Draw AF Construction
---------------------------------------------------------------------------------------------------------------------
Find G using Intersection Tool Intersecting Lines Postulate
---------------------------------------------------------------------------------------------------------------------
AF = FH by drawing a circle with F Construction
as the Center through point A
---------------------------------------------------------------------------------------------------------------------
EF || BH and FD || HC Midsegment Theorem
---------------------------------------------------------------------------------------------------------------------
FC || BH and FB || HC Substitution
---------------------------------------------------------------------------------------------------------------------
BFHC is parallelogram def of parallelogram
---------------------------------------------------------------------------------------------------------------------
BG GC Diagonals of parallelogram Bisect
--------------------------------------------------------------------------------------------------------------------- #
Statements Reasons
---------------------------------------------------------------------------------------------------------------------
Triangle ABC, D and E are midpoints, Given/ these constructions
BD and CE are medians
---------------------------------------------------------------------------------------------------------------------
Intersect G using intersection tool Intersecting Lines Postulate
---------------------------------------------------------------------------------------------------------------------
Draw AF Construction
---------------------------------------------------------------------------------------------------------------------
Find G using Intersection Tool Intersecting Lines Postulate
---------------------------------------------------------------------------------------------------------------------
AF = FH by drawing a circle with F Construction
as the Center through point A
---------------------------------------------------------------------------------------------------------------------
EF || BH and FD || HC Midsegment Theorem
---------------------------------------------------------------------------------------------------------------------
FC || BH and FB || HC Substitution
---------------------------------------------------------------------------------------------------------------------
BFHC is parallelogram def of parallelogram
---------------------------------------------------------------------------------------------------------------------
BG GC Diagonals of parallelogram Bisect
--------------------------------------------------------------------------------------------------------------------- #
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