Select the correct answer from each drop-down menu. the figure shows three parallelograms: abcd, a′b′c′d′, and a″b″c″d″. polygon abcd is to create parallelogram a′b′c′d′. polygon abcd is to create parallelogram a″b″c″d″.

answer: abcd

step-by-step explanation:

the first step is to draw a line from point b to line ad, such that the line makes a right angle with the line ad. we'll call the place where it meets ad point p. and the line we've drawn is bp.

now, we know that the height of the parallelogram is 4. so we know that line bp has a length of 4.

next, look at the triangle on the far right of the diagram. there's a point below point c in the diagram (where there's a right angle). let's call that point x. we know that triangle dcx is a right triangle, with sides 2 and 4.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.