The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)

The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.

Question

25-07-2022
Mathematics

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The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)

The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.

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pranavgera011 pranavgera011 · Answer 1 · 2022-07-26T22:42:10+02:00

The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.

Which conclusion is true about the quadrilaterals?

Given that,

vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)

vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)

(x,y) ; (x, y-8)

ABCD is reflected across the line y=4 to get the quadrilateral EFCD.

Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.

Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.

Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).

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