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

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### Use the Hinge theorem and complete the relationships in the given questions.

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### 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”?

### In the given figure AB = CD,

If ∠CAB > ∠DCA then,

### In the given figure AB = CD,

If ∠CAB > ∠DCA then,

### In the given figure AB = CD,

If AD > BC then,

### In the given figure AB = CD,

If AD > BC then,

### Indirect proof is also called ____

### Indirect proof is also called ____

### 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.

Centroid divides a median in the ratio 2:1

### If G is the centroid of triangle ABC,

Find BG.

BE= 12

### If G is the centroid of triangle ABC,

Find BG.

BE= 12

### 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.

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 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

>>>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.