obj. 21 medians, altitudes, and midsegments
DESCRIPTION
Identify altitudes and medians of triangles Identify the orthocenter and centroid of a triangle Use triangle segments to solve problems Identify a midsegment of a triangle and use it to solve problems.TRANSCRIPT
- 1. Obj. 21 Medians, Altitudes, MidsegmentsThe student is able to (I can): Identify altitudes and medians of triangles Identify the orthocenter and centroid of a triangle Use triangle segments to solve problems Identify a midsegment of a triangle and use it to solveproblems.
2. medianaltitudeA segment whose endpoints are a vertex ofthe triangle and the midpoint of theopposite side.A perpendicular segment from a vertex tothe line containing the opposite side. 3. centroid The intersection of the medians of atriangle. It is also the cccceeeennnntttteeeerrrr ooooffff mmmmaaaassssssss forthe triangle. 4. Centroid TheoremThe centroid of a triangle is locatedof the distance from each vertex tothe midpoint of the opposite side.GHJX YRZ= 22GR GY3= 2HR HZ3JR JX3=23 5. orthocenter The intersection of the altitudes of atriangle. 6. midsegment A segment that joins the midpoints of twosides of a triangle.HOTI CEPoints I, C, and E aremidpoints of DHOT.IC, CE, and EIare midsegments. 7. Triangle Midsegment TheoremA midsegment of a triangle is parallel toa side of the triangle, and its length ishalf the length of that side.HOTI CE1IC HT, IC HT2 = 8. Examples Find each measure.1. FEFE = 2(LT) = 2(14)= 282. mUFEFmUFE = mTSE= 623. UEUE = 2(9) = 18LUTES14444666622229LT and TSare midsegments.