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Dafna1 [17]
3 years ago
8

In ΔABC shown below, segment DE is parallel to segment AC: Triangles ABC and DBE where DE is parallel to AC The following two-co

lumn proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally: Statement Reason 1. Line segment DE is parallel to line segment AC 1. Given 2. Line segment AB is a transversal that intersects two parallel lines. 2. Conclusion from Statement 1. 3. ∠BDE ≅ ∠BAC 3. Corresponding Angles Postulate 4. 4. 5. 5. 6. BD over BA equals BE over BC 6. Converse of the Side-Side-Side Similarity Theorem Which statement and reason accurately completes the proof? 4. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate 5. ∠B ≅ ∠B; Reflexive Property of Equality 4. ∠B ≅ ∠B; Reflexive Property of Equality 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate 4. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate 5. ∠A ≅ ∠C; Isosceles Triangle Theorem 4. ∠A ≅ ∠C; Isosceles Triangle Theorem 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate

Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
8 0

Answer:

4.Angle B =Angle B

Reason: Reflexive property of equality

5.Triangle BDE is similar to triangle BAC

Reason: AA similarity postulate

Step-by-step explanation:

In triangle ABC

Segment DE is parallel to segment AC.

1.Segment DE is parallel to AC

Reason: Given

2.Line segment AB is a transversal line which intersects two parallel lines

Reason:Conclusion from statement 1

3.Angle BDE congruent to angle BAC

Reason: Corresponding angles postulate

4.Angle B =Angle B

Reason: Reflexive property of equality

5.Triangle BDE is similar to triangle BAC

Reason: AA similarity postulate

6.BD over BA equals BE over BC.

Reason:When two triangles are similar then the ratio of their corresponding sides are equal

storchak [24]3 years ago
5 0

Answer:

3. BDE is congruent to BAC; corresponding angles postulate

4. B is congruent to B; reflexive property of equality

Step-by-step explanation:

I took the test.

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Shoe sizes for men in the United States are known to follow a normal distribution. If you calculated the z-score of a man's shoe
anastassius [24]

Answer:

This value means that his shoe size is 2.9 deviations above the population mean.

And we can find the approximate percentile for his measure like this:

P(Z

This correspond to the 99.8 percentile, so then his shoe size is 99.8% above all the shoe sizes.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the shoe size of a population, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

Where \mu represent the mean and \sigma the population standard deviation.

For this case we know that a man obtain a z score of z=2.9

This value means that his shoe size is 2.9 deviations above the population mean.

And we can find the approximate percentile for his measure like this:

P(Z

This correspond to the 99.8 percentile, so then his shoe size is 99.8% above all the shoe sizes.

3 0
3 years ago
a club decides to sell t-shirts for $15.00 as a fundraiser. it costs $20.00 plus $9.00 per t-shirt to make the t-shirts. write a
Scilla [17]
The club would have to sell at least 6 t-shirts.
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3 years ago
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Nostrana [21]

Answer:

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Step-by-step explanation:

5 0
2 years ago
What is 0.8%of $5,700?
EastWind [94]

Answer: 0.8% of 5,700 = <u><em>45.6 </em></u>

Step-by-step explanation:

0.8% × 5,700 =

(0.8 ÷ 100) × 5,700 =

(0.8 × 5,700) ÷ 100 =

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5 0
3 years ago
Read 2 more answers
What 2 numbers multiply to -147 but add to -14?
Bezzdna [24]
Okay, so let's go over multiplying negative numbers.  A positive times a positive is a positive, right?  But a negative times a negative is also a positive.  Only a negative times a positive (or a positive times a negative) gives you a negative number.  So, we know that one of our 2 numbers in this question must be negative; the other must be positive.

Let's now take a look at the factors of -147, starting with the positives.  Obviously, -147 and 1 are factors: -147 * 1 = -147.  What other factors of -147 are there?

What about 7?  Try it: -147 / 7 = -21.  So here are two factors: -21, and 7.  They multiply to -147.  Do they add up to -14?  Let's see: -21+7 = 7+(-21) = 7-21= -14.  Yup, that works!

Answer: -21 and 7
4 0
3 years ago
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