Mathematics
Grade9
Easy
Question
Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”
- XYZ is not equiangular
- XYZ is not equilateral
- XYZ is obtuse-angled
- XYZ is a scalene triangle
Hint:
Contradiction of the statement generally includes not in the positive statement and remove not in the negative statement.
The correct answers are: XYZ is not equilateral, XYZ is obtuse-angled
Given That:
Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”
>>> let p, q are the two statements. Then, the the relation be p->q and the contradiction of the relation becomes p->~q
>>> Therefore, the contradiction of the statement if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle is:
If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.
.>>> Therefore, the triangle is not an equilateral triangle.
If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.
Related Questions to study
Mathematics
Write the contradictory assumption for “if a and b are even numbers, then a + b is an even number.”
Write the contradictory assumption for “if a and b are even numbers, then a + b is an even number.”
MathematicsGrade9
Mathematics
What is the temporary assumption to prove that A is an obtuse angle by proof of contradiction?
What is the temporary assumption to prove that A is an obtuse angle by proof of contradiction?
MathematicsGrade9
Mathematics
Use the Hinge theorem and complete the relationships in the given questions.
Use the Hinge theorem and complete the relationships in the given questions.
MathematicsGrade9
Mathematics
Use the Hinge theorem and complete the relationships in the given questions.
Use the Hinge theorem and complete the relationships in the given questions.
MathematicsGrade9
Mathematics
Use the Hinge theorem and complete the relationships in the given questions.
Use the Hinge theorem and complete the relationships in the given questions.
MathematicsGrade9
Mathematics
Use the Hinge theorem and complete the relationships in the given questions.
Use the Hinge theorem and complete the relationships in the given questions.
MathematicsGrade9
Mathematics
Use the Hinge theorem and complete the relationships in the given questions.
Use the Hinge theorem and complete the relationships in the given questions.
MathematicsGrade9
Mathematics
What is the temporary assumption used to prove that “If a + b ≠ 18, and a = 16 then b ≠ 2”?
What is the temporary assumption used to prove that “If a + b ≠ 18, and a = 16 then b ≠ 2”?
MathematicsGrade9
Mathematics
In the given figure AB = CD,
If ∠CAB > ∠DCA then,
In the given figure AB = CD,
If ∠CAB > ∠DCA then,
MathematicsGrade9
Mathematics
In the given figure AB = CD,
If AD > BC then,
In the given figure AB = CD,
If AD > BC then,
MathematicsGrade9
Mathematics
Indirect proof is also called ____
Indirect proof is also called ____
MathematicsGrade9
Mathematics
If G is the centroid of triangle ABC,
Find GD.
Centroid divides a median in the ratio 2:1
If G is the centroid of triangle ABC,
Find GD.
MathematicsGrade9
Centroid divides a median in the ratio 2:1
Mathematics
If G is the centroid of triangle ABC,
Find BG.
BE= 12
If G is the centroid of triangle ABC,
Find BG.
MathematicsGrade9
BE= 12
Mathematics
If G is the centroid of triangle ABC,
Find BE.
BG = 4x + 4
BG = 2/3 BE
4x + 4 = 2/3 (7x + 5)
12x + 12 = 14x + 10
2x = 2
x = 1
BE = 7x + 5
= 12
If G is the centroid of triangle ABC,
Find BE.
MathematicsGrade9
BG = 4x + 4
BG = 2/3 BE
4x + 4 = 2/3 (7x + 5)
12x + 12 = 14x + 10
2x = 2
x = 1
BE = 7x + 5
= 12
Mathematics
If G is the centroid of triangle ABC,
Find CG
>>>CG was given as 5x+1 and CF can be found in terms of x.
>>>There is no scope to find the value of x.
>>>Hence, we have no way to find the value of CG.
If G is the centroid of triangle ABC,
Find CG
MathematicsGrade9
>>>CG was given as 5x+1 and CF can be found in terms of x.
>>>There is no scope to find the value of x.
>>>Hence, we have no way to find the value of CG.
