2. Why are the triangles congruent?
2 answers:
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Answer
Find out the value of AM.
To prove
As given
In ABC,
centroid D is on median AM.
AD = x + 5 and DM = 3x – 5.
By using the centroid property
The centroid divides each median in a ratio of 2:1.
Thus D divide the median AM in a ratio of 2:1.
Therefore
(AD) = 2DM
(x + 5) = 6x – 10
5x = 15
x = 3
Now
AM = 3+ 5
= 8 unit
DM = 3 × 3- 5
= 4 unit
AM = AD + DM
= 8 + 4
AM = 12 unit
Therefore the AM is 12 unit.