Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M,...
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Transcript of Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M,...
![Page 1: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/1.jpg)
Warm Up
Write the converse, inverse, and contrapositive of:
“If M is the midpoint of AB, then M, A, and B are collinear.”
Are these statements true or false?
![Page 2: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/2.jpg)
• Converse: If M, A, and B are collinear, then M is the midpoint of AB
• Inverse: If M is not the midpoint of AB, then M, A, and B are noncollinear.
• Contrapositive: If M, A, and B are noncollinear, then M is not the midpoint of AB.
False
False
True
![Page 3: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/3.jpg)
ProbabilityProbability
How to solve probability.How to solve probability.
![Page 4: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/4.jpg)
Where do we use probability?
Insurance companies, card players, casino, lottery etc…
Who uses probability?
Doctors, secretaries, accountants, programmers, and GEOMETRY STUDENTS! Just to name a few.
Setting up and solving probability problems requires precise and orderly organized thinking skills.
![Page 5: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/5.jpg)
Probability is not part of geometry but rather statistics. However, you will see problems in the “Problems Sets” that deal with it, so follow these two basic
steps:
1. Determine all possibilities in a logical manner. Count them.
2. Determine the number of these possibilities that are “favorable”. We shall call these winners.
![Page 6: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/6.jpg)
List all possibilities:
A B C D
Calculate Probability:Probability = number of winners
number of possibilities
Ex. 1a. If one point is picked at random from the given figure, what is the probability that it is on the angle?
AB
C
D circle the winners.
P= = 1
100% it will happen!
4
4
![Page 7: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/7.jpg)
Ex. 1b. If two are picked at random, what is the probability they lie on ray CA?
AB
C
D
Order possibilities!
AB BC CD
AC BD
AD
Remember AB is the same as BA
Circle winners.
P =
= or 1:2 or 50%
3
6
1
2
![Page 8: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/8.jpg)
Ex. 2 What is the probability of picking Point Q on AC and it be within 5 units of B?
A CB
-20 7 10
Find the probability by comparing the length of the “winning” region
![Page 9: Warm Up Write the converse, inverse, and contrapositive of: “If M is the midpoint of AB, then M, A, and B are collinear.” Are these statements true or.](https://reader036.fdocuments.in/reader036/viewer/2022081908/56649e9f5503460f94ba17c1/html5/thumbnails/9.jpg)
Total numbers between -20 and 10 = 30
Within 5 units of B = 8
P = winnerspossibilities
=
=
8
30
4
15