Because ABCD is isosceles, we understand the reduced base angles space congruent and also the top base angles are congruent. This method ∠B is also 60° due to the fact that it"s paired up v ∠A together the lower base angle.

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Since quadrilaterals have internal angles that add up to 360°, we know m∠A + m∠B + m∠C + m∠D = 360°. Plugging in 60° for m∠A and also m∠B gives us m∠C + m∠D = 240°. Due to the fact that these two angles are additionally congruent as the top base pair of angles, every one is same to 120°.

Therefore, m∠C = 120°.


In a trapezoid, a pair the base angles are always congruent. Is this true or false? Why?

A trapezoid is a quadrilateral with just one pair that parallel sides. Basic angles can be congruent, but they don"t have come be. For this reason the declare is false. In one isosceles trapezoid, a pair the base angles are constantly congruent, but no other trapezoid is forced to fulfill this criterion.


Prove the the diagonals of a trapezoid perform not bisect each other.

See the word, "not"? If you weren"t thinking indirect proof, you need to be now. We can prove this by contradiction. We will certainly assume that a trapezoid has actually diagonals that do bisect each other and also show that it leads to 2 contradicting statements.

Let a trapezoid have diagonals bisect every other. If that"s the case, then the trapezoid is additionally parallelogram because any quadrilateral that has diagonals that bisect each various other is a parallelogram. But a parallelogram has two bag of opposite, parallel sides. This contradicts the an interpretation of a trapezoid, which deserve to have only one pair the parallel sides.

This way our presumption that the diagonals bisect each other cannot perhaps be true for a trapezoid.


PQ is the typical of trapezoid BCDF. Given the info in the figure, uncover y in terms of x.

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We recognize the mean of a trapezoid has actually a length that"s fifty percent the size of the sum of the bases. In other words, the size of the median is

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. The two bases FD and BC have lengths of x – 2 and x + 2, respectively. The median has actually a length of y. All we must do is plug ours values into the equation and isolate because that y.