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Shalnov [3]
3 years ago
6

1. What is the reason for Statement 3 of the two-column proof?

Mathematics
2 answers:
blagie [28]3 years ago
5 0

Answer:

#1) Angle Addition Postulate; #2) Definition of bisect; #3) postulate, definition and conjecture; #4) Given, Segment Addition Postulate, Subtraction Property of Equality; #5) Angle Addition Postulate, 60°+40°=m∠ABC, 100°=m∠ABC, Definition of obtuse angle.

Step-by-step explanation:

The angle addition postulate says that when two angles have a common vertex and common side, the measures of the smaller two angles added together is equal to the measure of the larger angle formed by the two.  In Statement 3 of Problem 1, JMK and KML are added to form JML.  This is the angle addition postulate.

When a segment or a line bisects an angle, it cuts it into two equivalent angles.  This is why the angles formed by bisector PQ, RPQ and QPS, are congruent.

Postulates, definitions, conjectures and theorems can all be used as reasons in a two-column proof.  Premises are not.

In #4, we are given that KL = MN.  LN is formed by pieces LM and MN; this is the segment addition postulate.  Once we have KL+LM = LM+MN, we can subtract LM from both sides; the property that allows us to do this is the subtraction property of equality.

In #5, we see that ∠ABC is formed by angles ABD and DBC; this is the angle addition postulate.  ABC = 60° and DBC = 40°; we substitute these in for the angles, using the substitution property.  We can then add these two angles together for a measure of 100°.  This is by definition an obtuse angle.  

OLEGan [10]3 years ago
3 0

1. Angle addition postulate (this could be wrong)

2. Definition of bisect

3. Definition and postulate

4. Screenshot at the bottom

Last one I can't help, my bad.

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The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3
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Dot plots are used to represent data using dots

The true statements about the dataset are:

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The dataset is given as:

4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1

Rearrange in ascending order

0, 0, 1, 1, 2, 2, 2, 2, 4, 4, 5, 6

Represent as a frequency table

Data     Frequency

0               2

1                2

2                4

3               0

4               2

5               1

6               1

See attachment for the dot plot

From the attachment, we can see that:

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  • 5 has a frequency of 1

Also, the range on the dot plot can be 0 to 7, because it covers the given dataset

Hence, the true statements are: (a), (b) and (c)

Read more about dot plots at:

brainly.com/question/21862696

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3 years ago
~**Will mark brainliest **~<br> For the correct answers to all three questions
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a)

\dfrac{42}{65}\cdot\dfrac{25}{36}\cdot\dfrac{26}{49}=\dfrac{2\cdot3\cdot7}{5\cdot13}\cdot\dfrac{5\cdot5}{2\cdot2\cdot3\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\dfrac{7}{13}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\\\\\\=\dfrac{1}{1}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2}{7}=\dfrac{5}{3}\cdot\dfrac{1}{7}=\dfrac{5}{21}

b)

\dfrac{21}{32}\cdot\dfrac{39}{120}\cdot\dfrac{40}{65}=\dfrac{21}{32}\cdot\dfrac{3\cdot13}{2\cdot2\cdot2\cdot3\cdot5}\cdot\dfrac{2\cdot2\cdot2\cdot5}{5\cdot13}=\\\\\\=\dfrac{3\cdot7}{32}\cdot\dfrac{13}{2\cdot2\cdot2\cdot5}\cdot\dfrac{2\cdot2\cdot2}{13}=\dfrac{21}{32}\cdot\dfrac{1}{5}\cdot\dfrac{1}{1}=\dfrac{21}{160}

c)

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6 0
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