Proving Vertical Angles Are Congruent RE
Statements Reasons
✓x
Given: 22 and 24 are vertical
angles.
Prove: 223 24
def. of a linear pair
subtraction property
substitution property
angle addition postulate
m
Reasons
1
1. given
2
Statements
✓ 1.22 and 24 are vert. angles
2. lines m and n intersect at P
3. 22 and 23 are a linear pair
n
P
2. def. of vertical angles
3. def. of a linear pair
4
3

David must install fencing around a lot that is shaped like a right angle.the side of lot that runs east-west is 200 ft long.the side of the lot runs north-south is 125 ft long.calculate how many feet of fencing he will need to surround the entire lot.

Find the solutions for a triangle with a =16, c =12, and b = 63º

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.