4.6 Medians of a Triangle - Murrieta Valley Unified School ...

1 Of a Triangle207 Goal Identify Medians Words median of a Triangle centroidA cardboard Triangle will balance on the end of a pencil if the pencil is placed at a particular point on the Triangle . Finding balancing points of objects is important in engineering, construction, and science. Ais a segment from a vertex to the midpoint of the opposite side. median of a of a TriangleCopy the Triangle and draw a TSTR, draw a median from Sto itsopposite side opposite aSis TR&*.Find the midpoint of TR&*, and label itP. Then draw a segment from point Sto point P. SP&*is a median of a MedianDraw a Median564 STR5334 STRP medianmedianmedianPage 1 of 5 Eis the centroid of TABCand DA527.

2 Find EAand Theorem , you know that EA5}23}DA5}23}(27) use the Segment Addition Postulate to find Addition Postulate275DE11827 2185DE118 218 Subtract 18 from each EA&*has a length of 18 and DE&*has a length of 27 for DAand18 for the Centroid of a Triangle AEDBCI ntersection of Medians of a TriangleWordsThe Medians of a Triangle intersect at the centroid, a point that is two thirds of the distance from each vertex to themidpoint of the opposite Pis the centroid of TABC, thenAP5}23}AD, BP5}23}BF, and CP5}23} following theorem tells you that the three Medians of a triangleintersect at one point. This point is called the of the the centroid of TQRSand RP510.

3 Find the length of RT&*. SolutionRP5}23}RTUse Theorem }23}RTSubstitute 10 for RP.}32}(10)5}32}1}23}RT2 Multiply each side by }32}. The median RT&*has a length of the Centroid of a Triangle 208 Chapter 4 Triangle RelationshipsMOREEXAMPLESMore examples HelpIC L A S S Z O N E . C O MPTPSR10 Page 2 of of a Triangle209In Exercises 1 and 2, complete the segment from a vertex of a Triangle to the midpoint of theopposite side is a(n) __? __?__ is the point where the three Medians TABC, then draw the median from point Ato BC&*.BD&*is a median of TABC. Find the length of AD&*. the centroid of TPQRand the centroid of TABCand PS533.

4 Find PTand Find BDand CheckVocabulary CheckGuided centroid of the Triangle is shown. Find the lengths. BEand ED, JGand KG, PQand PN, the Centroid of a Triangle1089 BACPage 3 of 5210 Chapter 4 Triangle RelationshipsIn Exercises 9 and 10, copy the Triangle and draw the three mediansof the a CentroidPis the centroid of TLMN. Find PNand a CentroidDis the centroid of TABC. Find CDand AnalysisDis the centroid of TABC. Your friend wants to find DE. The median AE518. Find and correct the error. Explainyour a CentroidDraw a Triangle and find the midpoint of eachside. Then draw the three Medians of your Triangle . Label thecentroid and ApplicationsExample 1:Exs.

5 9, 10, 18 Example 2:Exs. 11 13,17 Example 3:Exs. 14 16 Homework HelpExtra PracticeSee p. 5}32}AEDE 5}32}(18)DE 512 BEACDPage 4 of 5 Using AlgebraCopy the graph the coordinates of Q, R,and S, the midpoints of the sides of the the length of each the coordinates of thecentroid. Label this point as ChoiceIn the figure shown, Nis the centroid of TJKLandKM536. What is the length of MN&&? ChoiceIn the figure shown, Pis the centroid of TRST and PT512. What is the length of VT&*?XF8XG18XH24XJ36 Finding Angle Measures in a TriangleFind ma1. (Lesson ) Equivalent FractionsWrite two fractions equivalent to thegiven fraction. (Skills Review, p.)

6 656)30.}12}31.}15}32.}34}33.}184}34.}122 6}35.}220}36.}386}37.}4150}38.}1345}39.} 1284}40.}2300}41.}3243}Algebra Skills3281158140843816586081358160812584 581 Mixed ReviewStandardized TestPractice2yx10R P(5, 6)M(21, 22)N(11, 2) of a Triangle211 JMKLNRVSUPTWHOMEWORKHELPE xtra help with problemsolving in Exs. 19 21 is at HelpIC L A S S Z O N E . C O MPage 5 of 5