If z is the centroid of angle RST, RZ= 42, ST= 74, TW= 51, ZY=23 and find each measure
1 answer:
Check the picture below.
now, keep in mind that, a median, comes out of the vertices, and cuts the opposite side in two equal halves, thus is called a median.
now, there are 3 vertices, there are 3 medians, now they all meet at the centroid.
when they meet, the centroid cuts each median in a 2:1 ratio, so one side is twice as long as the small one.
with that in mind, we know ST = 74, therefore XT is just one of the halves, 74/2.
we know TW = 51, and we know the centroid cuts it in a 2:1 ratio, so if we divide 51 by 3, 2 pieces go to TZ and 1 piece to ZW. 51/3 = 17, so TZ takes 2 of those pieces or 17+17.
well, you know what ZW gets by now anyway.
we know RZ = 42, and we also know because of the 2:1 ratio, RZ is twice as large as XZ, so XZ is half of RZ, or 42/2.
we know ZY = 23, and because of the 2:1 ratio, we know ZY is smaller piece so SZ is twice as large, so SZ is 23*2. Therefore SY is just ZY + SZ.
now, keep in mind that, a median, comes out of the vertices, and cuts the opposite side in two equal halves, thus is called a median.
now, there are 3 vertices, there are 3 medians, now they all meet at the centroid.
when they meet, the centroid cuts each median in a 2:1 ratio, so one side is twice as long as the small one.
with that in mind, we know ST = 74, therefore XT is just one of the halves, 74/2.
we know TW = 51, and we know the centroid cuts it in a 2:1 ratio, so if we divide 51 by 3, 2 pieces go to TZ and 1 piece to ZW. 51/3 = 17, so TZ takes 2 of those pieces or 17+17.
well, you know what ZW gets by now anyway.
we know RZ = 42, and we also know because of the 2:1 ratio, RZ is twice as large as XZ, so XZ is half of RZ, or 42/2.
we know ZY = 23, and because of the 2:1 ratio, we know ZY is smaller piece so SZ is twice as large, so SZ is 23*2. Therefore SY is just ZY + SZ.
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