If one side of a triangle is 10 cm and another side is 6 cm. Find the possible length of the third side, if the third side is the longer side.

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

Can we draw a triangle for side lengths 5, 4, and 10 units? If so, mention the reason.

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?