2. If P is any point on side AB of triangle ABC and F, K, E are the midpoints of AP, PB, and PC, prove that AFKE ~ AABC. "Exercise 4.14 #10: If the hypotenuse and a leg of one right triangle are proportional to the hypotenuse and a leg of another, then the two triangles are similar. A4 c' a' T' c' - Given: b b' - Prove: AT ~ AT' Statements Reasons Statements Reasons 1. (see above) 1. Given a2 is b2 5. Subtraction a'2 %| b'2 Transformation 2. If 4 quantities are in proportion, then like powers are in proportion. c2 c'2 a2 b2 6. Alternation %3D b2 b'2 b'2 Transformation 3. c2 = a2 + b2; c'2 = a'2 + b'2 7. If 4 quantitie proportion, the are in proportic b. 3. Pythagorean Theorem b' a' a?+b2 4. b2 a'2+b'2 %3D b'2 4. Substitution (step 3 -> 2) 9. AT ~ AT' 9. 1.1. 6. 7. 2.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
The question is in the picture. Also, there is an example of how it should look like/how it should be done in the second picture.
![2. If P is any point on side AB of triangle
ABC and F, K, E are the midpoints of AP,
PB, and PC, prove that AFKE ~ AABC.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfeaa5ba-a58f-44a0-9ce8-a5047f1d9289%2Fcd6b47a1-f921-445b-be71-c4098376ce5d%2F5foa6z.jpeg&w=3840&q=75)
!["Exercise 4.14 #10: If the hypotenuse and a
leg of one right triangle are proportional to
the hypotenuse and a leg of another, then
the two triangles are similar.
A4
c'
a'
T'
c'
- Given:
b
b'
- Prove: AT ~ AT'
Statements
Reasons
Statements
Reasons
1. (see above)
1. Given
a2
is
b2
5. Subtraction
a'2
%|
b'2
Transformation
2. If 4 quantities are in
proportion, then like
powers are in proportion.
c2
c'2
a2
b2
6. Alternation
%3D
b2
b'2
b'2
Transformation
3. c2 = a2 + b2;
c'2 = a'2 + b'2
7. If 4 quantitie
proportion, the
are in proportic
b.
3. Pythagorean Theorem
b'
a'
a?+b2
4.
b2
a'2+b'2
%3D
b'2
4. Substitution (step 3 -> 2) 9. AT ~ AT'
9. 1.1.
6.
7.
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfeaa5ba-a58f-44a0-9ce8-a5047f1d9289%2Fcd6b47a1-f921-445b-be71-c4098376ce5d%2Fsrxnrcq.jpeg&w=3840&q=75)
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