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 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?

$A C equals 6 x minus 5 table attributes columnspacing 1em end attributes row cell equals 6 open parentheses 5 over 3 close parentheses minus 5 end cell row cell equals 5 end cell row cell text As end text x greater than 5 over 3 comma space A C greater than 5 end cell end table table attributes columnspacing 1em end attributes row blank end table$

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?

$x greater than 5 over 3$

Apply the Hinge theorem and converse and solve the following.

Find the possible values of x?

$x greater than 5 over 3$

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 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 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

Use the Hinge theorem and its converse and solve the following

What can be the x-value?

X < 9

Use the Hinge theorem and its converse and solve the following

What is the possible measure of ∠ACB?

As $x less than 14 comma straight angle A C B equals 56 to the power of ring operator$

Use the Hinge theorem and its converse and solve the following

What is the possible measure of ∠ACB?

As $x less than 14 comma straight angle A C B equals 56 to the power of ring operator$

Use the Hinge theorem and its converse and solve the following

what can be the x value?

5x + 6 < 76
5x < 70
x < 14

Use the Hinge theorem and its converse and solve the following

what can be the x value?

5x + 6 < 76
5x < 70
x < 14

Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”

If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.

Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”

If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.

Write the contradictory assumption for “if a and b are even numbers, then a + b is an even number.”

What is the temporary assumption to prove that A is an obtuse angle by proof of contradiction?

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

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