Worksheet: Inequality in One Triangle: Angle–Side

In this worksheet, we will practice identifying the relationships between angles and side lengths in a triangle to deduce the inequality in one triangle.

Q1:

Which is the correct relationship between 𝐴𝐢 and 𝐴𝐡?

  • A 𝐴 𝐢 > 𝐴 𝐡
  • B 𝐴 𝐢 = 𝐴 𝐡
  • C 𝐴 𝐢 < 𝐴 𝐡

Q2:

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

  • A 𝐴 𝐡 < 𝐢 𝐡
  • B 𝐴 𝐡 > 𝐢 𝐡
  • C 𝐴 𝐢 < 𝐢 𝐡
  • D 𝐴 𝐡 > 𝐴 𝐢

Q3:

Complete the following using <, =, or >: If, in the triangle 𝐷𝐸𝐹, 𝐷𝐸>𝐸𝐹, then π‘šβˆ πΉπ‘šβˆ π·.

  • A =
  • B >
  • C <

Q4:

Given 𝐴𝐡=92cm, 𝐴𝐢=91cm, and 𝐢𝐸=𝐡𝐷, choose the correct relationship between π‘šβˆ π΄πΈπ· and π‘šβˆ π΄π·πΈ.

  • A π‘š ∠ 𝐴 𝐸 𝐷 = π‘š ∠ 𝐴 𝐷 𝐸
  • B π‘š ∠ 𝐴 𝐸 𝐷 < π‘š ∠ 𝐴 𝐷 𝐸
  • C π‘š ∠ 𝐴 𝐸 𝐷 > π‘š ∠ 𝐴 𝐷 𝐸

Q5:

Choose the correct relationship between 𝐴𝐷 and 𝐴𝐡.

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

Q6:

Use <, =, or > to fill in the blank: π‘šβˆ πΈπ·π΄π‘šβˆ π΄πΆπ΅.

  • A =
  • B <
  • C >

Q7:

Use <, =, or > to fill in the blank: π‘šβˆ π΄π΅πΈπ‘šβˆ π΄πΆπ·.

  • A <
  • B =
  • C >

Q8:

Use <, =, or > to complete the sentence: If 𝐴𝐡𝐢 is a triangle and a point 𝐷 lies outside the triangle, then 𝐴𝐡+𝐴𝐢+𝐡𝐢2(𝐷𝐴+𝐷𝐡+𝐷𝐢).

  • A =
  • B >
  • C <

Q9:

Which of the following is true?

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

Q10:

Use <, =, or > to fill in the blank: Ifthenπ‘šβˆ π΄π΅π‘€<π‘šβˆ π΄πΆπ‘€,π‘šβˆ π΄π΅πΆπ‘šβˆ π΄πΆπ΅.

  • A =
  • B >
  • C <

Q11:

Which inequality is satisfied by this figure?

  • A π‘š ∠ 𝐢 < π‘š ∠ 𝐡 < π‘š ∠ 𝐡 𝐴 𝐢
  • B π‘š ∠ 𝐷 𝐴 𝐢 < π‘š ∠ 𝐡 < π‘š ∠ 𝐢
  • C π‘š ∠ 𝐡 < π‘š ∠ 𝐡 𝐴 𝐢 < π‘š ∠ 𝐢
  • D π‘š ∠ 𝐡 𝐴 𝐢 < π‘š ∠ 𝐢 < π‘š ∠ 𝐷 𝐴 𝐢
  • E π‘š ∠ 𝐷 𝐴 𝐢 < π‘š ∠ 𝐡 < π‘š ∠ 𝐡 𝐴 𝐢

Q12:

Arrange the side lengths of △𝐴𝐢𝐷 in descending order.

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

Q13:

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

  • A >
  • B =
  • C <

Q14:

List the sides of △𝐴𝐢𝐷 from shortest to longest.

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

Q15:

Use <, =, or > to fill in the blank: If π‘šβˆ πΆπ΅π·=π‘šβˆ πΆπ·π΅, then π‘šβˆ π΄π΅πΆπ‘šβˆ π΄π·πΆ.

  • A <
  • B =
  • C >

Q16:

Use <, =, or > to complete the following: In a triangle 𝐴𝐡𝐢, if 𝐷 is any point on 𝐡𝐢, then 𝐡𝐷+𝐷𝐢+2𝐴𝐷𝐴𝐡+𝐴𝐢.

  • A =
  • B <
  • C >

Q17:

Use <, =, or > to fill in the blank: If π‘šβˆ π΄πΆπ΅>π‘šβˆ π΄π΅πΆ, then π‘šβˆ π΄π΅π‘‹π‘šβˆ π΄πΆπ‘Œ.

  • A =
  • B <
  • C >

Q18:

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

  • A =
  • B <
  • C >

Q19:

Use <, =, or > to complete the statement: If 𝐴𝐡=62, 𝐴𝐢=63, and π‘šβˆ π΄π‘‹π‘Œ=π‘šβˆ π΄π‘Œπ‘‹, then π‘ŒπΆπ‘‹π΅.

  • A <
  • B =
  • C >

Q20:

Use <, =, or > to complete the following: If 𝐴𝐸>𝐸𝑋, then π‘šβˆ πΆπ‘šβˆ π·π΅πΆ.

  • A <
  • B >
  • C =

Q21:

Use <, =, or > to complete the statement: If π‘šβˆ π΄πΆπ΅=62∘ and π‘šβˆ π΄=57∘, then π‘šβˆ π΄π΅π·π‘šβˆ π΄πΆπ·.

  • A =
  • B >
  • C <

Q22:

Is ∠𝐴𝐷𝐢<,=,>∠𝐴𝐢𝐡?

  • A <
  • B >
  • C =

Q23:

Arrange 𝐴𝐢, 𝐴𝐷, 𝐢𝐷, 𝐢𝐡 in ascending order according to their lengths.

  • A 𝐢 𝐷 , 𝐴 𝐢 , 𝐴 𝐷 , 𝐢 𝐡
  • B 𝐴 𝐢 , 𝐢 𝐷 , 𝐴 𝐷 , 𝐢 𝐡
  • C 𝐢 𝐡 , 𝐴 𝐷 , 𝐢 𝐷 , 𝐴 𝐢
  • D 𝐴 𝐷 , 𝐢 𝐡 , 𝐢 𝐷 , 𝐴 𝐢
  • E 𝐢 𝐷 , 𝐴 𝐢 , 𝐢 𝐡 , 𝐴 𝐷

Q24:

Choose the correct relationship between 𝐴𝐡 and 𝐴𝐷.

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

Q25:

Complete the following using <, =, or >: π‘šβˆ πΉπΆπ·π‘šβˆ π΅πΉπΆ.

  • A <
  • B >
  • C =

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