In the diagram, number abcd is a transformation of number pmno. Name the segment i beg your pardon is congruent to bc. Afternoon no mn po

The trapezoid ABCD is rotated by part angle about some allude to kind the trapezoid PMNO.

Basic nature of Rotations:

1. A rotation maps a heat to a line, a ray to a ray, a segment come a segment, and an edge to one angle.

2. A rotation preservation lengths the segments.

3. A rotation preserves levels of angles.

4. As soon as parallel lines room rotated, their photos are likewise parallel.

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Un trapezoid ABCD lines ab and CD space parallel, in trapezoid present PM and also ON room parallel. Angle ∠B and ∠M space equal and angles ∠C and ∠N. This means that the rotation picture of BC is MN.

Correct an option is C.

The price is line segment MN. The points in the quadrilateral is PMNO however when you rotate the quadrilateral, it"s points when rotated is ABCD. BC and also MN room congruent based native the number given. Congruent sides space lines that has the same size of the sides.

In the provided image, first black line is drawn.

Then an arc through green shade is draw on the black line.

Then by same width that the compass draw an additional arc above.

And reduced the eco-friendly arc by exact same angle top top the black line.

And then attract a yellow line.

We can see those are equivalent angles equal.

So, the lines would be parallel.

So, correct alternative is : D. Parallel lines.

A. 29 because of the A^2+B^2=C^2B. 69 because you add up your lengths for the full lengthC. Radius? (im not certain on the one)D. It"s a parallel (rectangle or square) since side ad is equal to next BC and side ab is same to side DC

Part A:

From the appearance of the number above, triangle A B C creates a ideal angle in ~ B through A B and B C gift the legs and also A C being the hypothenuse.

Given the A B is 20 and B C is 21, by the pythagoras theorem,

Part B:

From the appearance of the figure above, triangle A B C develops a rightangle at B with A B and also B C as the legs and A C together the hypothenuse.

If this is true, climate the measure up of edge A B C is 90 degrees.

Part C:

If A E is 10 and also A F is half of A C, the unique name because that segment E F as it relates to triangle A B C is the midsegment.

The midsegment that a triangle is a heat segment which join the midpoints of 2 sides of the triangle.

Part D:

Given from part C over that line segment EF is a midsegment that triangle ABC, from the triangle midsegment theorem, line segment EF is parallel to next BC.

Thus, heat BF is a transverse that parallel currently EF and also BC which renders angle EFB alternative to angle FBC.

Since alternate angles space equal, provided that angle EFB is 43.6°, climate the measure up of edge FBC is likewise 43.6° since they are alternative angles.

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Part E:

If Triangle DCB is congruent come triangle ABC, then angle B is congruent to angle C.Given from component B that angle B = 90 degrees, then angle C = 90 degrees. Thus, the two nearby angles the the square ABCD = 90 degrees. Whih reflects that the form ABCD is a rectangle.