Question
Show the conjecture is false by finding a counterexample. Two adjacent angles always form a linear pair.
The correct answer is: Hence, the counterexample for the given conjecture is the above figure.
Linear pairs are always supplementary but adjacent angles may not be. It can be shown by the following
diagram:
Here, we can see that the sum of adjacent angles will be definitely less than 180o. So, the given conjecture is wrong.
Final Answer:
Hence, the counterexample for the given conjecture is the above figure.
Related Questions to study
Prove that ∠ ABC ≅ ∠ ADC
Prove that ∠ ABC ≅ ∠ ADC
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If they paid the same amount, how much was each cup of coffee?
Prove that ∠ ABC ≅ ∠ PQR
Prove that ∠ ABC ≅ ∠ PQR
Show the conjecture is false by finding a counterexample. If 
≅ 
, then point B is the midpoint of AB.
Show the conjecture is false by finding a counterexample. If ≅ , then point B is the midpoint of AB.
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
A store discounted the price of Doritos $0.35 and then a man bought 5 bags. If he paid a total of $12.70 for the bags of chips, how much was each bag originally?
Use the Law of Detachment to make a valid conclusion in the true situation.
If the measure of an angle is less than 90°, then it is an acute angle.
Use the Law of Detachment to make a valid conclusion in the true situation.
If the measure of an angle is less than 90°, then it is an acute angle.
Find JK
Find JK
A girl bought two packs of gum from the store. Later she thought she would need some more gum and went back to the store to buy three more packs of gum. If she paid a total of $5.70 for gum, how much was each pack of gum?
A girl bought two packs of gum from the store. Later she thought she would need some more gum and went back to the store to buy three more packs of gum. If she paid a total of $5.70 for gum, how much was each pack of gum?
Use the Law of Detachment to make a valid conclusion in the true situation.
If angles form a linear pair, then they are supplementary.
∠𝐴 𝑎𝑛𝑑 ∠𝐵 form a linear pair.
Use the Law of Detachment to make a valid conclusion in the true situation.
If angles form a linear pair, then they are supplementary.
∠𝐴 𝑎𝑛𝑑 ∠𝐵 form a linear pair.
A man buys four books from the store and a Preferred Reader discount card for $20. Later that day, he goes back and buys five more books. He also got a $5 discount using his new card. If he spent a total of $87 at the bookstore, how much did each book cost assuming every book cost the same amount?
A man buys four books from the store and a Preferred Reader discount card for $20. Later that day, he goes back and buys five more books. He also got a $5 discount using his new card. If he spent a total of $87 at the bookstore, how much did each book cost assuming every book cost the same amount?
Show the conjecture is false by finding a counterexample. If the product of two numbers is even, then the two numbers must be even.
Show the conjecture is false by finding a counterexample. If the product of two numbers is even, then the two numbers must be even.
Dimple Bought a Calculator and binder that were both 15% off the original price. The
original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the
original price of the calculator?
The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.
¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.
¶Steps to writing Variable Equation
1) Identify the variables that represent the unknowns.
2) Convert the issue into variable expressions in algebra.
3) Determine the variables' values to solve the equations for their true values.
Dimple Bought a Calculator and binder that were both 15% off the original price. The
original price of binder was Rs 6.20. Justin spent a total of Rs 107. 27 . What was the
original price of the calculator?
The x + 2 = 6 x+2=6x, plus, 2, equals 6 contains a variable. We call this type of equation with a variable an algebraic equation. Finding the variable value that will result in a true equation is typically our aim when solving an algebraic equation.
¶Variables or constants are the two types of measurable quantities. A variable is a quantity with a varying value, and the constant value is nothing but a constant.
¶Steps to writing Variable Equation
1) Identify the variables that represent the unknowns.
2) Convert the issue into variable expressions in algebra.
3) Determine the variables' values to solve the equations for their true values.
