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Dafna11 [192]
3 years ago
8

What is the reason for Statement 5 of the two-column proof?

Mathematics
2 answers:
zmey [24]3 years ago
8 0

Given: ∠JNL and ∠MNK are vertical angles and  m∠MNK=90°

Prove: ∠JNL is a right angle.

   Statements                                                     Reasons

1.  ∠JNL and ∠MNK are vertical angles.             Given

2. \angle JNL \cong \angle MNK        Vertical angle theorem

3. m \angle JNL = m \angle MNK        Angle congruence postulate

4.  m \angle MNK = 90^\circ                Given

5. m \angle JNL = 90^\circ                 <u> Substitution Property of Equality</u>

Since, the measures of angle JNL and MNK are equal and the measure of angle MNK is 90 degrees. therefore, by substitution property of equality, both the angles JNL and MNK will have an equal measure.

Therefore,  m \angle JNL = 90^\circ

6. ∠JNL is a right angle.                                     Definition of right angle

saveliy_v [14]3 years ago
6 0

Answer:D

Step-by-step explanation:

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Explanation:


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To rationalize that kind of expressions, this is to eliminate the radicals on the denominator you use conjugate rationalization.

That is, you have to multiply both numerator and denominator times the conjugate of the denominator.

The conjugate of √3+√6 is √3 - √6, so let's do it:

\frac{ \sqrt{3} - \sqrt{6} }{ \sqrt{3} + \sqrt{6} } . \frac{ \sqrt{3}- \sqrt{6}  }{ \sqrt{3}- \sqrt{6} }

To help you with the solution of that expression, I will show each part.

1) Numerator: (√3 - √6) . (√3 - √6) = (√3 - √6)^2 = (√3)^2 - 2√3√6 + (√6)^2 =

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2) Denominator: (√3 + √6).(√3 - √6) = (√3)^2 - (√6)^2 = 3 - 6 = - 3

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 9 - 6√2
-----------
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