I wil mark as brain list(and plz someone genuinely answer plz)

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

Answer:

Alternate angles form a 'Z' shape and are sometimes called 'Z angles'. ... d and f are interior angles. These add up to 180 degrees (e and c are also interior). Any two angles that add up to 180 degrees are known as supplementary angles.

If the transversal cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two angles shown always add to 180°.

Corresponding angles are equal. ... Adjacent angles add up to 180 degrees. (d and c, c and a, d and b, f and e, e and g, h and g, h and f are also adjacent). d and f are interior angles.

We also know that consecutive angles are supplementary, and 90 + 90 = 180. Therefore, all four angles would have a measurement of 90-degrees.

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4 years ago

Read 2 more answers

Determine whether quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1) is a trapezoid.

lisabon 2012 [21]

Answer:

We are given a quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

Step 1:

We find the slope of side AB.

with vertices A(-4,-5) and B(-3,0)

Hence, the slope of two points (a,b) and (c,d) is calculates as:

$\dfrac{d-b}{c-a}$

So, the slope of AB is:

$\dfrac{0-(-5)}{-3-(-4)}\\\\=\dfrac{5}{-3+4}\\\\=\dfrac{5}{1}=5$

Hence slope AB=5.

Step 2:

Now we have to find the slope of DC.

with vertices D(5,1) and C(0,2)

So, the slope of DC is:

$\dfrac{2-1}{0-5}\\\\=\dfrac{1}{-5}=-\dfrac{1}{5}$

Hence slope AB=-1/5.

Step 3:

slope of BC with vertices B(-3,0) and C(0,2) is:

$\dfrac{2-0}{0-(-3)}\\\\=\dfrac{2}{3}$

Step 4:

slope of AD with vertices A(-4,-5) and D(5,1) is:

$=\dfrac{1-(-5)}{5-(-4)}\\\\=\dfrac{1+5}{5+4}\\\\=\dfrac{6}{9}\\\\=\dfrac{2}{3}$

As we know that parallel sides have same slope.

As slope of BC=AD.

Hence AD is parallel to BC.

and the slope of two opposite sides are not equal hence the two sides are not parallel.

Hence, the given quadrilateral ABCD is a trapezoid. ( since it has a pair of opposite sides which are parallel and a pair of non-parallel opposite sides)