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.
You are watching: Diagonals of a trapezoid bisect each other
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. | |
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 . 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. |