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Volgvan
2 years ago
15

The base angle theorem is written as a conjecture,"if two sides of a triangle are congruent, then the angles opposite of them ar

e congruent". Write the converse of the conjecture and determine if it is true.
Mathematics
1 answer:
diamong [38]2 years ago
8 0

Step-by-step explanation:

Statement:

"If two sides of a triangle are congruent, then the angles opposite of them are congruent"

Converse:

If two angles of a triangle are congruent, then the two sides opposite them are congruent.

The converse of the statement is true and can be proven true using a two-column proof. In fact it is a theorem.

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Answer:

Step-by-step explanation:

What i would do is turn the first one into an improper fraction

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it's easier to multiply this way

see if you can simplify any of the terms first

7     1

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none of the numbers can be broken down further so we just multiply straight across

7 x 1 is 7

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the numbers 1,2,3,4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacet. find t
Tresset [83]

Consider such events:

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B - the sum of numbers is 4.

You have to count Pr(A|B).

Use formula for conditional probability:

Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}.

1. The event A\cap B consists in selecting two slips, first is 3 and second should be 1, because the sum is 4. The number of favorable outcomes is exactly 1 and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event A\cap B is

Pr(A\cap B)=\dfrac{1}{20}.

2. The event B consists in selecting two slips with the sum 4. The number of favorable outcomes is exactly 2 (1st slip 3 and 2nd slip 1 or 1st slip 1 and 2nd slip 3) and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event B is

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Answer: \dfrac{1}{2}.

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