Maths-
General
Easy
Question
Use the Law of Detachment to make a valid conclusion in the true situation. If two angles have the same measure, then they are congruent
![m straight angle A equals m straight angle B.](data:image/png;base64,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)
Hint:
Law of Detachment states that if p
q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.
The correct answer is: Hence we can conclude that Angle A and angle B are congruent angles.
Consider the statement into two separate statements
p: Two angles have the same measure
q: Two angles are congruent
So we can write the given statement “If two angles have the same measure, then they are congruent” as:
![p not stretchy rightwards arrow q](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAMCAYAAAAUNi9wAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAASpJREFUeNpjYECAeiCuBuJGIH4OxD+AeD8QSzKQB2qBWIUE9TxAPAmIP0DtXgPEU4C4HF3hKiC+C5UQBGImIO4D4uVkOhSk7xMQRxKhlgkaKIlQNh804P4DcQC64ltArIUmxge1jBwgDsRnoJbNBmIOAqFfjkUc5CZpdB99w6KQg4BD/5OAV+Ex5zE06gm6yRwa9OjAEoj3UiFEZwIxGw51BkB8EIs4VjeB0tF8LIqLoNFCyzQaBMSLsYhjddMkaEJGBqAQuESHXB+AI1mAHJ+GLrgOmnBdoHxpqFgiA+0BFxBfgyYBEDAG4i1A/BSIvdAVv4P6DOTYP0B8AVuxQEMgDg0YUPl5HIgdoW7iQI/idwyDC7BBC34U4AX1zWACWN0UD81MgwlguAkAWfNLnKcoi0EAAAB1dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnA8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWk+cTwvbWk+PC9tYXRoPrroo94AAAAASUVORK5CYII=)
We are given
![m straight angle A equals m straight angle B](data:image/png;base64,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)
which means angle A and angle B has the same measure so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e. angle A and angle B are congruent angles.
Final Answer:
Hence we can conclude that Angle A and angle B are congruent angles.
Related Questions to study
Maths-
Classify the equation 3x - x + 4 = 4(2x - 1) as having one solution , no solution or infinitely many solutions .
Classify the equation 3x - x + 4 = 4(2x - 1) as having one solution , no solution or infinitely many solutions .
Maths-General
Maths-
The Population of one town is 43,425. About 125 people move out of the town each month. Each month 200 people on average move into town. A nearby town has a population of 45000. It has no one moving in and an average of 150 people moving away every month. In about how many months will the population of the towns be equal ?
The Population of one town is 43,425. About 125 people move out of the town each month. Each month 200 people on average move into town. A nearby town has a population of 45000. It has no one moving in and an average of 150 people moving away every month. In about how many months will the population of the towns be equal ?
Maths-General
Maths-
The Weight of Abhi’s dog can be found using the expression 2(x+3), where x is the number of weeks. The weight of tarun’s dog can be found using the expression3(x + 1), where x is the number. Will the dogs ever be the same weight ? explain.
The Weight of Abhi’s dog can be found using the expression 2(x+3), where x is the number of weeks. The weight of tarun’s dog can be found using the expression3(x + 1), where x is the number. Will the dogs ever be the same weight ? explain.
Maths-General
Maths-
Make and test a conjecture about the sum of two even numbers.
Make and test a conjecture about the sum of two even numbers.
Maths-General
Maths-
How many solutions does this equation have 2(6x+9-3x) = 5x+21
How many solutions does this equation have 2(6x+9-3x) = 5x+21
Maths-General
Maths-
Solve the equation -2.6b + 4 = 0.9b - 17
Solve the equation -2.6b + 4 = 0.9b - 17
Maths-General
Maths-
Sunil has Rs 450 in her savings account . she deposits Rs 40 each month. Arun has Rs 975 in his checking account. He writes a check for Rs 45.90 each month for his cell phone bill. He also writes a check for Rs 19.55 each month for his water bill. After how many months will Sunil and Arun have the same amount of money in their accounts ?
Sunil has Rs 450 in her savings account . she deposits Rs 40 each month. Arun has Rs 975 in his checking account. He writes a check for Rs 45.90 each month for his cell phone bill. He also writes a check for Rs 19.55 each month for his water bill. After how many months will Sunil and Arun have the same amount of money in their accounts ?
Maths-General
Maths-
Vihan’s class is making care packages to give to victims of a natural disaster. Vihan packs one box in 5 minutes and has already packed 12 boxes. His friend Simaran packs one box in 7 minutes and has already packed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?
Vihan’s class is making care packages to give to victims of a natural disaster. Vihan packs one box in 5 minutes and has already packed 12 boxes. His friend Simaran packs one box in 7 minutes and has already packed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?
Maths-General
Maths-
Make a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.
Make a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.
Maths-General
General
Express
as a power with base 3.
Express
as a power with base 3.
GeneralGeneral
Maths-
Arun and Kiran work in a banquet hall. Arun earns a 20% commission on his food sales. Kiran earns a weekly salary of Rs 625 plus a 10% commission on his food sales . What amount of food sales will result in Arun and Kiran earning the same amount for the week ?
Arun and Kiran work in a banquet hall. Arun earns a 20% commission on his food sales. Kiran earns a weekly salary of Rs 625 plus a 10% commission on his food sales . What amount of food sales will result in Arun and Kiran earning the same amount for the week ?
Maths-General
Maths-
Make a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Make a conjecture about the sum of numbers from 1 to 7. Write a conjecture for the general case.
Maths-General
Maths-
Solve the equation 96 - 4.5x - 3.2x = 5.6x + 42.80
Solve the equation 96 - 4.5x - 3.2x = 5.6x + 42.80
Maths-General
Maths-
Kishore earns a weekly salary of Rs 925 and a 5% commission on his total sales. Neeraj earns a weekly salary of Rs. 1250 and a 3% commission on sales. What amount of sales will result in them earning the same amount for the week?
Kishore earns a weekly salary of Rs 925 and a 5% commission on his total sales. Neeraj earns a weekly salary of Rs. 1250 and a 3% commission on sales. What amount of sales will result in them earning the same amount for the week?
Maths-General
Maths-
Make and test a conjecture about the square of even numbers
Make and test a conjecture about the square of even numbers
Maths-General