Because ABCD is isosceles, we know the reduced base angles space congruent and the top base angles are congruent. This method ∠B is also 60° because it"s combine up v ∠A together the lower base angle.

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Since quadrilaterals have actually internal angles that include up come 360°, we recognize m∠A + m∠B + m∠C + m∠D = 360°. Plugging in 60° for m∠A and m∠B offers us m∠C + m∠D = 240°. Because these two angles are likewise congruent as the upper base pair that angles, each one is same to 120°.

Therefore, m∠C = 120°.


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

A trapezoid is a square with just one pair the parallel sides. Basic angles might be congruent, but they don"t have to be. Therefore the declare is false. In one isosceles trapezoid, a pair that base angles are always congruent, however no various other trapezoid is compelled to accomplish this criterion.


Prove that the diagonals that a trapezoid execute not bisect each other.

See the word, "not"? If girlfriend weren"t reasoning indirect proof, you need to be now. We have the right to prove this by contradiction. We will certainly assume that a trapezoid has diagonals that do bisect every other and show that it leads to two contradicting statements.

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

This way our assumption that the diagonals bisect each other cannot possibly be true because that a trapezoid.


PQ is the median of trapezoid BCDF. Provided the info in the figure, discover y in regards to x.

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We understand the mean of a trapezoid has actually a length that"s half the length of the sum of the bases. In other words, the length of the median is

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