After examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conc
lusion?
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem
2 answers:
The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
It is given the two triangles are similar.FG and TU are the medians of the triangle .
By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
So
Option D. Proportional Medians Theorem is the right answer.
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Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).