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dalvyx [7]
3 years ago
9

Mary states, If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Decide if her statement i

s true or false?

Mathematics
2 answers:
Mila [183]3 years ago
8 0
The answer for apex would be true.
Darina [25.2K]3 years ago
7 0

Answer:

True

Step-by-step explanation:

Let us consider a parallelogram ABCD in which AB=CD and AD=BC.

Now, from ΔABC and ΔBAD, we have

AD=BC (Opposite sides of parallelogram)

BD=AC (Given)

AB=BA (common)

Thus, by SSS rule of congruency,

ΔABC≅ΔBAD.

Now, by corresponding parts of congruent triangles, we have

∠ABC=∠BAD.

But, we know that ∠ABC and ∠BAD forms the corresponding angle pair, thus ∠ABC+∠BAD=180°

⇒2∠ABC=180

⇒∠ABC=90°

Since they are interior angles of parallel lines AC and BC on the same side of their common secant AB. They are therefore both right, and ABCD is a rectangle.

Hence, the statement If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle is true.

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What is the perimeter of the figure to the nearest tenth of a millimeter
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6. Sketch the region enclosed by the graphs of x =0, 6y-5x=0 and x+3y=21. Find the area
kow [346]
We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h

1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
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Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
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