Which statement best explains whether △pqr is congruent to △xyz? △pqr is congruent to △xyz because △pqr can be mapped to △xyz by a rotation of 180° about the origin. △pqr is congruent to △xyz because △pqr can be mapped to △xyz by a translation 5 units down followed by a reflection across the y-axis. △pqr is not congruent to △xyz because there is no sequence of rigid motions that maps △pqr to △xyz. △pqr is congruent to △xyz because △pqr can be mapped to △xyz by a reflection across the y-axis followed by a reflection across the x-axis.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12