Similar Triangles

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines

lisabon 2012 [21]

To enable the completion of the proof that line l is parallel to line m, a

diagram showing the lines and their common transversal is attached.

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ∠1 and ∠2 are supplementary angles ${}$ 1. Given

2. m∠1 + m∠2 = 180° ${}$ 2. Definition of supplementary ∠s

3. ∠1 and ∠3 are supplementary angles ${}$ 3. Exterior sides in opposite rays

4. m∠1 + m∠3 = 180° ${}$ 4. Definition of supplementary ∠s

5. m∠1 + m∠2 = m∠1 + m∠3 ${}$ 5. Transitive property of equality

6. m∠2 = m∠3 ${}$ 6. Subtraction property of equality

7. l ║ m ${}$ 7. Converse of alternate interior

${}$ angles postulate

Reasons:

Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°

Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)

Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles

Reason for statement 5: Transitive property of equality describes the property that if a number x = y, and z = y, then x = z.

Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality

Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.

Learn more here:

brainly.com/question/25178453

6 0

2 years ago

6.

larisa86 [58]

V=ca times height
1040=40 times h
H=1040 divide by 40
Height=26

3 0

3 years ago

Evaluate the expression below at x = 5. x/35 + 5x^2

kramer

Answer:

876/7

Step-by-step explanation:

Just plug the number 5 into the equation and solve. Remember your Order of Operations (PEMDAS).

4 0

2 years ago

For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the f

pishuonlain [190]

Answer:

The probability is 0.33696

Step-by-step explanation:

The probability that the outcome will be heads x times is calculated using the following equation:

$P(x) = nCx*p^{x} *(1-p)^{n-x}$

nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

This apply for variables that follows a binomial distribution. In which we have n independent and identical events with two possibles results: success and fail with a probability p and 1-p respectively.

So, In this case, n is equal to 5, and p is equal to 0.6 because we are going to call success the event in which the outcome of the coin is head.

Then, the probability that the outcome will be heads at least 4 times is calculated as:

P = P(4) + P(5)

Where P(4) is:

$P(4) = 5C4*0.6^{4} *(1-0.6)^{5-4}$

P(4)=0.2592

And P(5) is:

$P(5) = 5C5*0.6^{5} *(1-0.6)^{5-5}$

P(4)=0.07776

Finally, the probability is:

P = 0.2592 + 0.07776

P = 0.33696

5 0

3 years ago

Find the image of (3,8) after a reflection over the origin.

Oksana_A [137]

Answer:

(-3, -8) I think

Step-by-step explanation

over the origin mean it would be going diagonally across (0,0). Not directly down (over the x-axis/ across the y-axis), nor to the side (over y-axis/ across the x-axis

3 0

2 years ago