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Lesson: Triangle Inequality: Angle–Side Relationship Theorem

In this lesson, we will learn how to use the angle–side inequality in triangles and more complex figures.

Sample Question Videos

01:59
04:14
03:25

Worksheet • 24 Questions • 3 Videos

Q1:

Which is the correct relationship between 𝐴 𝐶 and 𝐴 𝐵 ?

  • A 𝐴 𝐶 < 𝐴 𝐵
  • B 𝐴 𝐶 > 𝐴 𝐵
  • C 𝐴 𝐶 = 𝐴 𝐵

Q2:

From the figure below, determine the correct inequality from the following.

  • A
  • B
  • C
  • D

Q3:

Complete the following using < , = , or > : If, in the triangle 𝐷 𝐸 𝐹 , 𝐷 𝐸 > 𝐸 𝐹 , then 𝑚 ∠ 𝐹 𝑚 ∠ 𝐷 .

  • A <
  • B >
  • C =

Q4:

Given 𝐴 𝐵 = 9 2 c m , 𝐴 𝐶 = 9 1 c m , and 𝐶 𝐸 = 𝐵 𝐷 , choose the correct relationship between 𝑚 ∠ 𝐴 𝐸 𝐷 and 𝑚 ∠ 𝐴 𝐷 𝐸 .

  • A 𝑚 ∠ 𝐴 𝐸 𝐷 < 𝑚 ∠ 𝐴 𝐷 𝐸
  • B 𝑚 ∠ 𝐴 𝐸 𝐷 > 𝑚 ∠ 𝐴 𝐷 𝐸
  • C 𝑚 ∠ 𝐴 𝐸 𝐷 = 𝑚 ∠ 𝐴 𝐷 𝐸

Q5:

Choose the correct relationship between 𝐴 𝐷 and 𝐴 𝐵 .

  • A 𝐴 𝐷 > 𝐴 𝐵
  • B 𝐴 𝐷 < 𝐴 𝐵
  • C 𝐴 𝐷 = 𝐴 𝐵

Q6:

Use < , = , or > to fill in the blank: 𝑚 ∠ 𝐸 𝐷 𝐴 𝑚 ∠ 𝐴 𝐶 𝐵 .

  • A <
  • B >
  • C =

Q7:

Use < , = , or > to fill in the blank: 𝑚 ∠ 𝐴 𝐵 𝐸 𝑚 ∠ 𝐴 𝐶 𝐷 .

  • A =
  • B >
  • C <

Q8:

Use < , = , or > to complete the sentence: If 𝐴 𝐵 𝐶 is a triangle and a point 𝐷 lies outside the triangle, then 𝐴 𝐵 + 𝐴 𝐶 + 𝐵 𝐶 2 ( 𝐷 𝐴 + 𝐷 𝐵 + 𝐷 𝐶 ) .

  • A =
  • B <
  • C >

Q9:

Which of the following is true?

  • A 𝐶 𝐹 < 𝐵 𝐹
  • B 𝐶 𝐹 > 𝐵 𝐹
  • C 𝐶 𝐹 = 𝐵 𝐹

Q10:

Use < , = , or > to fill in the blank:

  • A >
  • B <
  • C =

Q11:

Which inequality is satisfied by this figure?

  • A 𝑚 ∠ 𝐶 < 𝑚 ∠ 𝐵 < 𝑚 ∠ 𝐵 𝐴 𝐶
  • B 𝑚 ∠ 𝐵 < 𝑚 ∠ 𝐵 𝐴 𝐶 < 𝑚 ∠ 𝐶
  • C 𝑚 ∠ 𝐷 𝐴 𝐶 < 𝑚 ∠ 𝐵 < 𝑚 ∠ 𝐵 𝐴 𝐶
  • D 𝑚 ∠ 𝐷 𝐴 𝐶 < 𝑚 ∠ 𝐵 < 𝑚 ∠ 𝐶
  • E 𝑚 ∠ 𝐵 𝐴 𝐶 < 𝑚 ∠ 𝐶 < 𝑚 ∠ 𝐷 𝐴 𝐶

Q12:

Arrange the side lengths of △ 𝐴 𝐶 𝐷 in descending order.

  • A 𝐴 𝐶 , 𝐴 𝐷 , 𝐶 𝐷
  • B 𝐴 𝐷 , 𝐶 𝐷 , 𝐴 𝐶
  • C 𝐶 𝐷 , 𝐴 𝐶 , 𝐴 𝐷
  • D 𝐴 𝐶 , 𝐶 𝐷 , 𝐴 𝐷
  • E 𝐶 𝐷 , 𝐴 𝐷 , 𝐴 𝐶

Q13:

Use < , = , or > to fill in the blank: 𝐴 𝐶 𝐷 𝐵 .

  • A =
  • B >
  • C <

Q14:

List the sides of from shortest to longest.

  • A
  • B
  • C
  • D
  • E

Q15:

Use < , = , or > to fill in the blank: If 𝑚 ∠ 𝐶 𝐵 𝐷 = 𝑚 ∠ 𝐶 𝐷 𝐵 , then 𝑚 ∠ 𝐴 𝐵 𝐶 𝑚 ∠ 𝐴 𝐷 𝐶 .

  • A >
  • B <
  • C =

Q16:

Use < , = , or > to complete the following: In a triangle 𝐴 𝐵 𝐶 , if 𝐷 is any point on 𝐵 𝐶 , then 𝐵 𝐷 + 𝐷 𝐶 + 2 𝐴 𝐷 𝐴 𝐵 + 𝐴 𝐶 .

  • A =
  • B >
  • C <

Q17:

Use < , = , or > to fill in the blank: If 𝑚 ∠ 𝐴 𝐶 𝐵 > 𝑚 ∠ 𝐴 𝐵 𝐶 , then 𝑚 ∠ 𝐴 𝐵 𝑋 𝑚 ∠ 𝐴 𝐶 𝑌 .

  • A =
  • B >
  • C <

Q18:

Use < , = , or > to fill in the blank: 𝐵 𝐶 𝐴 𝐶 .

  • A =
  • B >
  • C <

Q19:

Use < , = , or > to complete the statement: If 𝐴 𝐵 = 6 2 , 𝐴 𝐶 = 6 3 , and 𝑚 ∠ 𝐴 𝑋 𝑌 = 𝑚 ∠ 𝐴 𝑌 𝑋 , then 𝑌 𝐶 𝑋 𝐵 .

  • A <
  • B >
  • C =

Q20:

Use < , = , or > to complete the following: If 𝐴 𝐸 > 𝐸 𝑋 , then 𝑚 ∠ 𝐶 𝑚 ∠ 𝐷 𝐵 𝐶 .

  • A =
  • B >
  • C <

Q21:

Use < , = , or > to complete the statement: If 𝑚 ∠ 𝐴 𝐶 𝐵 = 6 2 ∘ and 𝑚 ∠ 𝐴 = 5 7 ∘ , then 𝑚 ∠ 𝐴 𝐵 𝐷 𝑚 ∠ 𝐴 𝐶 𝐷 .

  • A >
  • B <
  • C =

Q22:

Is ∠ 𝐴 𝐷 𝐶 < , = , > ∠ 𝐴 𝐶 𝐵 ?

  • A =
  • B <
  • C >

Q23:

Arrange , , , in ascending order according to their lengths.

  • A
  • B
  • C
  • D
  • E

Q24:

Choose the correct relationship between 𝐴 𝐵 and 𝐴 𝐷 .

  • A 𝐴 𝐵 < 𝐴 𝐷
  • B 𝐴 𝐵 > 𝐴 𝐷
  • C 𝐴 𝐵 = 𝐴 𝐷
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