The angle opposite to the longer side is _____ in a triangle.

The sum of lengths of any two sides is ____ than the third side in a triangle.

What can be the length of AB?

AB > 46

What can be the length of AC?

Therefore, the Side AC should be greater than 58 degrees.

What do you observe in ∆ABC?

Right angled triangle:
The triangle in which one of the angle is being 90 degrees.
>>>Therefore, we can say that the given triangle is an example of right angled triangle.

Which group of lengths is used to form a triangle?

The sides that follows triangle inequality is (3,4,5).
>>>It forms right angled triangle.

Mention the smaller angle to the larger angle from the given figure.

The required relation between the angles of a given triangle is:
∠CBA < ∠CAB < ∠ACB

How can you say which angle is the largest in a triangle?

>>>By using the longest side largest angle theorem, we can find the largest angle in the triangle.

If one side of a triangle is 11 cm and another side is 6 cm. Find the possible length of the third side.

Let x be the length of the third side.
11 + 6 > x
17 > x
6 + x > 11
X > 5
The third side value can be greater than 5 and less than 17.

Mention the smaller side to the longer side from the given figure.

Therefore, for the given triangle the order of length of sides  AC < AB < BC.

Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the fourth statement of proof?

Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the second statement of proof?

Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the last statement of proof?

Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the third statement of proof?

Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the first statement of proof?

Apply the Hinge theorem to the given figure.