Determine whether or not the pairs of triangles are similar and explain why.
1 answer:
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Given:
The bases of a trapezoid lie on the lines
To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is
Where, m is slope and b is y-intercept.
On comparing with slope intercept form, we get
On comparing with slope intercept form, we get
The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.
The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.
So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get
Therefore, the equation of line that contains the midsegment of the trapezoid is .