Hinge Theorem Ordering Sides and Angles

Exterior Angle Inequality Theorem

by Robert Tinaro

​Exterior Angle Inequality Theorem

​The exterior angle of a triangle is greater than either remote interior angle.

Multiple Choice

Which of ∠1, ∠7, and ∠2 has the largest measure?

• ∠1

• ∠7

• ∠2

Multiple Choice

Which of ∠4, ∠5, and ∠1 has the largest measure?

• ∠4

• ∠5

• ∠1

Multiple Choice

Use the figure to determine which of the following angles has the greatest measure:  $$\angle\ 1,\ \angle\ 3,\ \angle4$$  

• $$\angle1$$  

• $$\angle3$$  

• $$\angle4$$  

• Not enough information

Multiple Choice

Use the figure to determine which of the following angles has the greatest measure:  $$\angle\ 4,\ \angle\ 8,\ \angle9$$  

• $$\angle4$$  

• $$\angle8$$  

• $$\angle9$$  

• Not enough information

​Inequalities of One Triangle

​

​The smallest angle of a triangle is opposite the shortest side. Conversely, the shortest side of a triangle is opposite the smallest angle. Overall, the angles or sides of a triangle can be ordered by the relative size of the angles or sides opposite them.

Multiple Choice

• WN, NP, WP
• NP, WN, WP
• WP, NP, WN
• WP, WN, NP

Multiple Choice

Find the largest angle in Δ PRQ

• ∠R
• ∠P
• ∠Q
• ∠S

​Triangle Inequality Theorem

​The sum of any 2 sides of a triangle must be greater than the third.

Multiple Choice

Can the following side measures form a triangle?
  3, 5, 8 

• Yes
• No

Multiple Choice

What is the range of values of x for a triangle's third side given side measures of 8 and 15?

• between 8 and 15
• between 7 and 23
• less than 7, greater than 23

Multiple Choice

9. Which of these lengths CANNOT represent the sides of a triangle?

• 32, 34, 60
• 28, 30, 58
• 13, 20, 27
• 2, 4, 5

​SAS Inequality Theorem

Multiple Choice

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

• Greater than
• Less than
• Equal to
• Half of 

Multiple Choice

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

• Less than
• Greater than
• Equal to 
• Half of

Multiple Choice

Select the correct answer

• A
• B
• C
• D

​Means-Extremes Theorem

​If two ratios are equivalent (proportional), then the cross-products are equal.

Multiple Choice

Find x

• 10.5
• 5
• 8.5
• 6

Multiple Choice

Solve the proportion.

• p=31.3
• p=308
• p=924
• p=532

Multiple Choice

Solve.
(2x - 3) / 4  = 9

• x = 24
• x = 12
• x = 17.5
• x = 19.5

Multiple Choice

Solve for b 

• 8
• 17/12
• 4/3
• 1/8

​Similar Polygons

​Two polygons are similar if and only if the corresponding angles are proportional and the corresponding sides are proportional.

Multiple Choice

Solve for x.

• 21
• 14
• 12
• 18

Multiple Choice

What is the zoom factor or scale factor from small to big of these 2 figures?

• $$\frac{3}{2}$$

• $$-\frac{3}{2}$$

• $$\frac{2}{3}$$

• $$-\frac{2}{3}$$

Multiple Choice

Solve for x. 

• 8
• 6
• 10
• 12

Multiple Choice

State if the polygons are similar.

• a

• b

• c

• d

Multiple Choice

The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger

figure.

• a

• b

• c

• d

​Similar Triangles

​AA Similarity

​

​SSS Similarity

​

​SAS Similarity

Multiple Choice

Are these triangles similar?

• Yes
• No

Multiple Choice

Are the triangles similar? If so, what is the scale factor from ΔDEF to ΔABC?

• Yes. 1.5

• Yes. ⅔

• Yes. 2

• No.

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

What is the measure of x?

• 12
• 15
• 6
• 9

Multiple Choice

Find x.

• 54/7
• 56/3
• 11
• 21/2

Multiple Choice

Choose the similarity statement for the triangles.

• ΔMNL ∼ ΔOPQ
• ΔNOM ∼ ΔPQL
• ΔLMN ∼ ΔPQO
• ΔMLN ∼ ΔPQO

Multiple Choice

Find the height of the tree.

• 8 ft
• 12 ft
• 13 ft
• 15 ft

Multiple Choice

• 24
• 16
• 30
• 50