A conjecture and the paragraph proof used to prove the conjecture are shown.
1 answer:
Observe the figure given.
Let us complete the given paragraph:
It is given that E is the midpoint of DF. So, DE by the definition of midpoint.
As, midpoint divides the line segment into two equal halves.
Therefore, DE =EF by the segment congruence postulate. DE+EF = DF by the segment addition postulate and so DE+DE = DF by substitution.
Segment Addition Postulate states that given 2 points P and Q, a third point S lies on the line segment PQ if and only if the distances between the points satisfy the equation PS + SQ = PQ.
Simplifying gives 2DE = DF.
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Answer:
54.6 cm : B
Step-by-step explanation:
Mathematically the area of a rectangle is 2( l + b)
So in practical terms we only need the measure of two sides as we have 2 equal sides for a rectangle.
We can see that we have two right angles on each sides
Now to find b, we can use trigonometric ratios
For each of the rectangles, the diagonal represents the hypotenuse
Mathematically;
sin 30 = b/20
From triangle ABC
b = 20 sin 30 = 20 * 0.5 = 10 cm
Now, to get l
Mathematically;
Sin 60 = l/20
l = 20 sin 60 = 17.32 cm
So the perimeter is;
2(10 + 17.32)
2(27.32) = 54.64 cm which is 54.6 to the nearest tenth
