Question

AB is parallel to CD. CD is rotated 180°. Which statement describes the relationship between C'D' and the transformed AB? How can you prove it?
A) C'D' intersects AB; Graph the points to find the point of intersection.

B) C'D' || AB; Use the slope formula to prove that the segments have the same slope.

C) C'D'≠AB; Use the distance formula to prove that the segments are not the same length.

D) C'D' ⊥ AB; Use the slope formula to prove that the segments have opposite reciprocated slopes.

Answer 1

Answer :- Statement (B) ,C'D' ll AB

Given AB is parallel to CD.  CD rotated$180^{\circ}$.

Consider a transversal line l intersecting AB and CD at angle x.

therefore By slope formula,

slope of AB and CD = m =tanx

Now after rotation of  $180^{\circ}$ CD become C'D'

therefore, slope of C'D' = $tan(x+180^{\circ})$=tanx=m

Hence C'D' ll AB.