To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, 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. <u>Definition of supplementary ∠s</u>
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. <u>m∠1 + m∠3 = 180° </u> 4. <u>Definition of supplementary ∠s</u>
5. m∠1 + m∠2 = m∠1 + m∠3 5. <u>Transitive property of equality</u>
6. <u>m∠2 = m∠3 </u> 6. <u>Subtraction property of equality</u>
7. l ║ m 7. <u>Converse of alternate interior </u>
<u>angles postulate</u>
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 <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.
- 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
Since 3/5 of the students wore blue shirts and 1/4 of the students wore white shirts, you need to find the Total of 3/5 and 1/4.
First, step find a common denominator for both fractions
EXAMPLE: 3/5+1/4=Total 3/5 becomes 12/20 and 1/4 becomes 5/20.
Second, notice that both fractions now have the same denominator, now you can find the sum of both fractions which is 17/20
Finally, you need to check if the fraction can be SIMPLIFIED if not then the fraction is already im simplest form.
THE ANSWER: 17/20 of students wore either a blue or white shirt on Friday
Answer: No Real Answers
Step-by-step explanation:
1. Distribute
4x-8=4x+10
2. Get variables to one side add 8, subtract 4x)
0 = 18
3. Since this statement is false, the answer is... No real answers
To solve this problem, we need to use the Pythagorean Theorem, which states that a^2 + b^2 must equal c^2. "a" is the length of one of the legs (shorter sides of the triangle) and "b" is the length of the other leg. "c" is the length of the hypotenuse.
a = y = 36.25cm
b = x = 20.93cm
a^2 + b^2 = c^2
(36.25)^2 + (20.93)^2 = c^2
1314.0625 + 438.0649 = c^2
√1752.1274 = √c^2
c = 41.8584209 ≈ 41.86
So your final answer is...
The length of the hypotenuse is about 41.86 cm.
Answer:
h
Step-by-step explanation:
