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## Constructions

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**Constructions**Centoids**Review of Prerquisite**To construct a perpendicular bisector you need a ... Fish. Let’s begin !**Medians**A Median is a segment connecting the vertex of a triangle to the opposite midpoint.**The medians of a triangle are concurrent at a point called**the centroid.**Construction of the Median**Start with the FISH to find a midpoint of side BC. Start with the base and point B.**Construct arc from point C past the midpoint of BC**Connect the arc intersection points to find the midpoint. Construct the median from A to the midpoint.**Construct arc from point A past the midpoint of BA**Connect the arc intersection points to find the midpoint. Construct the median from C to the midpoint.**It is not necessary to construct all three medians**because… Two intersecting lines determine a point. Centroid**It is only necessary to draw 2 medians.**The third median would only intersect the other lines at the same point. We will now look at several examples of centroids to solidify your understanding.**1**3 2 4**Construction of the Median**Start with the FISH to find a midpoint of side BC. Start with the base and point B.**Construct arc from point C past the midpoint of BC**Connect the arc intersection points to find the midpoint. Construct the median from A to the midpoint.**Construct arc from point A past the midpoint of BA**Connect the arc intersection points to find the midpoint. Construct the median from C to the midpoint.**It is not necessary to construct all three medians**because… Two intersecting lines determine a point. Centroid**When two medians intersect then they divide each other into**a small segment and a large segment. Let’s look at several situations.**The ratio is always 2:1**Therefore… 10 If DF = 5, then AD = _____ ? 5**10**If DF = 5, then AD = _____ ? 7**6**If AD = 12, then DF = _____ 12 ?**8**If AD = 16, then DF = _____ 16 ?**Summary**1. A Median is a segment connecting the vertex of a triangle to the opposite midpoint. 2. The three medians of a triangle are concurrent. 3. The point of concurrency is called a centroid.**Summary**4. When two medians intersect then they divide each other into a large segment and a small segment.**Summary**5. The centroid is always inside the triangle. 6. To construct the median you… You construct a fish on 2 sides. You connect the opposite vertex to the midpoint.**C’est fini.**Good day and good luck. That’s all folks. A Senior Citizen Production