Free Printable Hinge Theorem

1.

It is called the HINGE theorem, because...

a)

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

b)

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

c)

"hinge" is the Spanish word for angle.

d)

the triangle makes a hinge shape, like a tent.

2.

Compare $m\angle ACD\ and\ m\angle GDE$

a)

$m\angle ACB\ >\ m\angle GDE$

b)

$m\angle ACD\ <\ m\angle GDE$

c)

$m\angle ACB\ =\ m\angle GDE$

d)

$\angle ACB\ \cong\ \angle GDE$

3.

Compare QT and ST

a)

$QT\ <\ ST$

b)

$QT\ >\ ST$

c)

$QT\ =\ ST$

d)

$\overline{QT}\ \cong\ \overline{ST}$

4.

Find the range of possible values for x.

a)

$\frac{7}{2}<x<24$

b)

$x<6$

c)

$24<x$

d)

$\frac{11}{2}<x<6$

5.

Find the range of possible values of x.

a)

$\frac{5}{3}<x<8$

b)

$-\frac{3}{2}<x>8$

c)

$\frac{32}{3}<x<27$

d)

$27<x<37$

6.

Find the range of possible values for x.

a)

$2\ <x<6$

b)

$6<x<15\ \frac{1}{3}$

c)

$6<x<22$

d)

$2<x<22$

7.

Find the range of possible values of x.

a)

$-20<x<21$

b)

$8<x<37$

c)

$34<x<37$

d)

$8<x<24$

8.

Find the range of possible values for x

a)

$x>7$

b)

$-\frac{17}{3}<x>7$

c)

$-\frac{17}{3}<x<7$

d)

$x<7$

9.

Which inequality relates $\angle FBG\ and\ \angle BFA$ ?

a)

$m\angle FBG\ <m\angle BFA$

b)

$m\angle FBG\ >m\angle BFA$

c)

$m\angle FBG\ \ge m\angle BFA$

d)

$m\angle FBG\ \le m\angle BFA$

10.

Which inequality relates $\angle GBC\ and\ \angle FBA$ ?

a)

$m\angle GBC\ <m\angle FBA$

b)

$m\angle GBC\ >\ m\angle FBA$

c)

$m\angle GBC\ \le\ m\angle FBA$

d)

$m\angle GBC\ \ge\ m\angle FBA$

11.

Four students are doing a scavenger hunt starting at the water fountain. They disagree one the directions and split up. Their paths are shown in the diagram. Which pair is closest to the fountain when they stop?

a)

Luther and Stephanie

b)

Mario and Lee

12.

Which is NOT a possible measure for ∠DCB?

a)

27º

b)

30º

c)

34º

d)

35º

13.

Which of the following is a possible length for segment AC

a)

10

b)

15

c)

17

d)

9

14.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

15.

Select the correct answer

a)

A

b)

B

c)

C

d)

D

16.

Using the hinge theorem, we can say that AB _____ DC

a)

Greater than

b)

Less than

c)

Equal to

d)

Half of

17.

Using the hinge theorem, we can say that Angle 1 _____ Angle 2.

a)

Less than

b)

Greater than

c)

Equal to

d)

Half of

18.

Using the hinge theorem, we can say that Angle 1 _____ Angle 2.

a)

Less than

b)

Greater than

c)

Equal to

d)

Half of

19.

BC _____ EF

a)

<

b)

>

c)

=

d)

No conclusion can be made.

20.

What are the possible values for x?

a)

x < 16

b)

4 < x < 16

c)

x < 40

d)

4 < x < 40

Hinge Theorem

Total questions: 20

Worksheet time: 20mins

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