age of 4.6 edians of a riangle Goal Identify s in triangles. ey Words of a triangle centroid 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. of a triangle is a segment from a vertex to the midpoint of the opposite side. X raw a edian In, draw a from to its opposite side. 4 6 olution he side opposite a is &*. Find the midpoint of &*, and label it. hen draw a segment from point to point. &* is a of. 4 raw a edian opy the triangle and draw a.. 2.. 4 6 4.6 edians of a riangle 207
age 2 of he following theorem tells you that the three s of a triangle intersect at one point. his point is called the centroid of the triangle. HO 4.9 Intersection of edians of a riangle Words he s of a triangle intersect at the centroid, a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. F ymbols If is the centroid of, then 2, 2 F, and 2. Itudent Help I Z O. O O X ore examples at classzone.com X is the centroid of and 27. Find and. olution 2 Use the entroid of a riangle Using heorem 4.9, you know that 2 2 (27) 8. ow use the egment ddition ostulate to find. 27 8 egment ddition ostulate ubstitute 27 for and 8 for. 27 8 8 8 ubtract 8 from each side. 9 implify. W &* has a length of 8 and &* has a length of 9. X Use the entroid of a riangle is the centroid of Q and 0. Find the length of &*. olution 2 Use heorem 4.9. 0 2 ubstitute 0 for. 2 (0) 2 2 ultiply each side by 2. 0 implify. W he &* has a length of. 208 hapter 4 riangle elationships
age of Use the entroid of a riangle he centroid of the triangle is shown. Find the lengths. 4. Find and,. Find G and G, 6. Find Q and, given 24. given 4. given Q 20. H F G 4.6 xercises Guided ractice Vocabulary heck In xercises and 2, complete the statement.. he segment from a vertex of a triangle to the midpoint of the opposite side is a(n)?. 2. he? is the point where the three s intersect.. opy, then draw the from point to &*. 9 0 8 kill heck &* is a of. Find the length of &*. 4.. 6. 4 7. is the centroid of Q and 8. is the centroid of and. Find and. 2. Find and. 4.6 edians of a riangle 209
age 4 of ractice and pplications xtra ractice ee p. 682. In xercises 9 and 0, copy the triangle and draw the three s of the triangle. 9. F 0. G Using a entroid is the centroid of. Find and œ.. Q 9 2. Q 2. Q 0 Using a entroid is the centroid of. Find and. 4.. 6. 9 7. rror nalysis is the centroid of. Your friend wants to find. he 8. Find and correct the error. xplain your reasoning. 2 2 (8) 2 Homework Help xample : xs. 9, 0, 8 xample 2: xs., 7 xample : xs. 4 6 8. Finding a entroid raw a triangle and find the midpoint of each side. hen draw the three s of your triangle. abel the centroid. 20 hapter 4 riangle elationships
age of Itudent Help I Z O. O HOWO H xtra help with problem solving in xs. 9 2 is at classzone.com Using lgebra opy the graph shown. 9. Find the coordinates of Q,, and, the midpoints of the sides of the triangle. 20. Find the length of each. 2. Find the coordinates of the centroid. abel this point as. 2 (, 2) y (, 6) Π0 (, 2) x tandardized est ractice 22. ultiple hoice In the figure shown, is the centroid of and 6. What is the length of &&? 9 2 6 24 2. ultiple hoice In the figure shown, is the centroid of and 2. What is the length of V &*? F 8 G 8 H 24 6 V U W ixed eview Finding ngle easures in a riangle Find ma. (esson 4.2) 24. 2. 26. 4 2 60 27. 28. 29. 40 60 4 6 2 lgebra kills Writing quivalent Fractions Write two fractions equivalent to the given fraction. (kills eview, p. 66) 0. 2. 2. 4. 8 4 4. 2 26. 2 20 6. 8 6 7. 0 4 8. 4 9. 8 24 40. 2 0 0 4. 24 4.6 edians of a riangle 2