Similar triangles ABC and DEF are shown on the coordinate plane. Linet passes through points B, E, F, and C
Use the similar triangles to explain the relationship between the slopes of BC and
EF
Drag a response into each box to explain
The slope of BC equals
and the slope of EF equals
D
Since AABC is similar to ADEF and BC and EF both lie on line t, the slope of
A
BC is
greater than
the slope of EF
AB
AC
AC
203
BC
A
EF
DE
DF
DE
DE
DE
equal to
less than

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

1/125 probability for each student so, a 0.8 percent probably of winning per student.