In the diagram, figure abcd is a revolution of number pmno. Surname the segment i m sorry is congruent come bc. Afternoon no mn po

The trapezoid ABCD is rotated by part angle around some suggest 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 to a segment, and also an edge to an angle.

2. A rotation conservation lengths the segments.

3. A rotation preserves degrees of angles.

4. Once parallel lines room rotated, their photos are likewise parallel.

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Un trapezoid ABCD lines ab and CD are parallel, in trapezoid currently PM and ON are parallel. Angle ∠B and also ∠M room equal as well as angles ∠C and also ∠N. This way that the rotation photo of BC is MN.

Correct choice is C.

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

In the given image, very first black line is drawn.

Then one arc through green color is attract on the black line.

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

And cut the eco-friendly arc by exact same angle on the black color line.

And then attract a yellow line.

We have the right to see those are corresponding angles equal.

So, the lines would be parallel.

So, correct choice is : D. Parallel lines.

A. 29 due to the fact that of the A^2+B^2=C^2B. 69 due to the fact that you add up your lengths for the complete lengthC. Radius? (im not certain on the one)D. It"s a parallel (rectangle or square) because side advertisement is same to next BC and also side abdominal is same to side DC
Part A:

From the appearance of the number above, triangle A B C creates a right angle in ~ B v A B and also B C gift the legs and A C gift 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 forms a rightangle in ~ B through A B and B C together the legs and A C together the hypothenuse.

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

Part C:

If A E is 10 and A F is half of A C, the unique name for segment E F as it relates come triangle A B C is the midsegment.

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

Part D:

Given from part C above that heat segment EF is a midsegment that triangle ABC, native the triangle midsegment theorem, line segment EF is parallel to side BC.

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

Since alternative angles space equal, provided that edge EFB is 43.6°, climate the measure up of angle FBC is also 43.6° because they are alternating angles.

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Part E:

If Triangle DCB is congruent to triangle ABC, climate angle B is congruent to edge C.Given from component B that angle B = 90 degrees, climate angle C = 90 degrees. Thus, the two surrounding angles of the quadrilateral ABCD = 90 degrees. Whih reflects that the shape ABCD is a rectangle.