How can you say which angle is the largest in a 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.

Apply the Hinge theorem and converse and solve the following.

Find AB, if BD = 9?

Apply the Hinge theorem and converse and solve the following.

Find the possible value of BD, if AC = 7

Apply the Hinge theorem and converse and solve the following.

Find the possible value of AC?

Apply the Hinge theorem and converse and solve the following.

Find the possible values of x?

Use the Hinge theorem and its converse and solve the following

What is the possible measure of MN, if MP = 20?

The length of MN = 5x + 3
= 5(2) + 3 = 13

Use the Hinge theorem and its converse and solve the following

What is the possible measure of MP?

Therefore, the length of  MP>48.

Use the Hinge theorem and its converse and solve the following

What can be the x-value?

X < 9