Hinge Theorem and Inequalities in a Triangle

Which of the following is a possible  length for segment AC

• 10

• 15

• 17

• 9

What are the possible values for x?

• x < 16

• 4 < x < 16

• x < 40

• 4 < x < 40

It is called the HINGE theorem, because...

• the vertex of the angle acts like a hinge to open the triangle.

• it's named after Joseph Hinge, the man who discovered it.

• "hinge" is the Spanish word for angle.

• the triangle makes a hinge shape, like a tent.

Compare measure of angle Y and measure of angle M.

• measure of angle Y = measure of angle M

• measure of angle Y > measure of angle M

• measure of angle Y < measure of angle M

• Not enough information is given.

Name the angles from SMALLEST to LARGEST

• Q, R, P

• P, Q, R

• R, P, Q

• R, Q, P

• >

• <

• =

Select all that are TRUE.

• AB > AE

• BE > CE

• BE > CD

• CD < DE

• CE > BC

What are the possible values for the third side of the triangle if two sides are 23 & 16

• 16 < x < 23

• 7 < x < 39

• 7 > x > 39

• 8 ≤ x ≤ 38

Which is the range of values of "x" for the triangle shown?

Name the sides from SMALLEST to LARGEST

• RS, ST, TR

• ST, RT, RS

• RT, ST, RS

• RT, RS, ST