Write a two-column proof. If point g is the centriod of triangle ABC and BG = 18. Find GE and BE.
My work:
ge is half so its 9.
be equals 18 + 9 = 27
i need help on two column proof part
1.ace is good
2.acp is good
3.acp is good
4. edp is good
9 + 20 is 29 bro put 9 is half and pur 29 is fulll bro u got me
Sure! Here is a two-column proof for the given problem:
Statement Reason
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1. BG = 18 Given
2. GE is half of BG Definition of centroid
3. GE = 18/2 = 9 Substitution
4. BE = BG + GE Definition of centroid
5. BE = 18 + 9 = 27 Substitution
Let's break down the steps:
1. Statement 1 is given in the problem: BG = 18.
2. Statement 2 follows from the definition of a centroid, which states that the centroid divides each median into two segments such that the segment closer to the vertex is twice as long as the segment closer to the opposite side. Therefore, GE is half of BG.
3. Statement 3 is the result of substituting the value of BG from statement 1 into the equation GE = BG/2, which gives GE = 18/2 = 9.
4. Statement 4 follows from the definition of a centroid, which states that the centroid is the point of concurrency of medians. Therefore, BE is equal to the sum of BG and GE.
5. Statement 5 is the result of substituting the values of BG = 18 and GE = 9 into the equation BE = BG + GE, which gives BE = 18 + 9 = 27.
Hence, the two-column proof shows that GE is 9 and BE is 27.