Question
Name the theorem or postulate that justifies the given statement.
∠1 ≅ ∠2
Hint:
identify the position of angles 1 and angle 2 and name the postulate .
The correct answer is: Vertical angles theorem or vertically opposite angles theorem
ANS :- Vertical angles theorem or vertically opposite angles theorem
Explanation :-
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
Related Questions to study
A rope joins the points P ≡ (-10, 5) and Q ≡ (6, 9). At which point should we cut the rope to get two equal parts?
A rope joins the points P ≡ (-10, 5) and Q ≡ (6, 9). At which point should we cut the rope to get two equal parts?
The parallel sides of a trapezium are in the ratio 3:4. If the distance between the parallel sides is 9cm and the area is 126cm2, find the length of its parallel sides.
The parallel sides of a trapezium are in the ratio 3:4. If the distance between the parallel sides is 9cm and the area is 126cm2, find the length of its parallel sides.
The functions f and g are defined by f(x) = 4x and g(x)= x2. For what value of x does f (x)– g( x) =4 ?
Note:
Instead of solving the equation 
in the above way, we could also use the quadratic formula, given by
Where the quadratic equation is given by
Or we could simply observe that it the expression of a perfect square
The functions f and g are defined by f(x) = 4x and g(x)= x2. For what value of x does f (x)– g( x) =4 ?
Note:
Instead of solving the equation in the above way, we could also use the quadratic formula, given by
Where the quadratic equation is given by
Or we could simply observe that it the expression of a perfect square
Find the co-ordinates of the mid-point of AB, if A ≡ (1, 10) and B ≡ (3, -8).
Find the co-ordinates of the mid-point of AB, if A ≡ (1, 10) and B ≡ (3, -8).
The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.
The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.
Note:
Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
Note:
Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
Find the value of x that satisfies the equation 7x + 22 = − 27 .
Find the value of x that satisfies the equation 7x + 22 = − 27 .
The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?
The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?
Joe’s age is 16 years less than 5 times Jim’s age. Find Jim’s age if Joe is 9 years old.
Joe’s age is 16 years less than 5 times Jim’s age. Find Jim’s age if Joe is 9 years old.
Are the two polygons congruent? Explain why or why not.
Are the two polygons congruent? Explain why or why not.
Which of the following expressions is equivalent to the expression above?
Note:
Another way of solving this problem is to expand all the terms in the expression
Then we get,
Thus, we will get that
Can be written as
This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.
Which of the following expressions is equivalent to the expression above?
Note:
Another way of solving this problem is to expand all the terms in the expression
Then we get,
Thus, we will get that
Can be written as
This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.
