PLEASE HELP. In the triangles below, DF MN, DG MP, D P. Can you prove that DFG MNP? Explain your answer. (15 points)
1 answer:
Complete question is;
In the triangles attached , DF is congruent to MN,DG is congruent to MP, angle D is congruent to angle P. Can you prove that triangle DFG is congruent to MNP.
Answer:
Proved below
Step-by-step explanation:
From the attached triangles, we can see that;
∠D corresponds to ∠M
∠F corresponds to ∠N
∠G corresponds to ∠P
But we are told that ∠D is congruent to ∠P. Thus, since we have 2 other congruent sides in the triangles, we can conclude that Side-Angle-Side Postulate (SAS) congruency theorem that triangle DFG is congruent to MNP.
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Note: Let us consider, we need to find the gradient of line L.
Given:
The given equation of a line is:
The line L passes through the points with coordinates (- 3, 1) and (2, - 2).
To find:
The gradient of the given line and the gradient of line L.
Solution:
Slope intercept form of a line is:
...(i)
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the gradient of the given line is -4.
The line L passes through the points with coordinates (- 3, 1) and (2, - 2). So, the gradient of line L is:
Therefore, the gradient of the line L is .