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Laabri

7.4 Triangle Inequality Theorem (Due 4/25/24)

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Review

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Day 2 4/25/24

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Isosceles and Equilateral Triangles

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Essential Question: How can you use inequalities to describe the relationships among side lengths and angle measures in a triangle?

Learning Target: Students will be able to describe the relationships among triangle sides using side lengths and measures and use that information to solve real-world problems.

Complete the entire document and use full sentences when prompted for full credit.

Responses without work will receive no points.

Asemmisa {{asɛmmisaAhyɛnsode}}
1.

Determine if each group of three side is a triangle.

Triangle

Not a Triangle

16 m, 21 m, 39 m

18 in, 6 in, 13 in

34 km, 27 km, 58 km

29 ft, 38 ft, 9 ft

12 cm, 12 cm, 25 cm

31 yd, 14 yd, 19 yd

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2.

Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

14 and 22

a) Set up difference and sum that shows the possible range of side lengths for the third side

- <third side (x) < +

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

< x <

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3.

Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

31 and 28

a) Set up difference and sum that shows the possible range of side lengths for the third side

- <third side (x)< +

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

< x <

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4.

Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

24 and 7

Write the inequality the shows the range of lengths that could be a third side this triangle:

< x <

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5.

Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

8 and 17

Write the inequality the shows the range of lengths that could be a third side this triangle ( use <x< )

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6.

How many integer values of x are there so that x, 5, and 8 could be the lengths of the sides of a triangle?

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7.

How many integer values of x are there so that x, 12, and 6 could be the lengths of the sides of a triangle?

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8.

A plot of land is in the shape of rhombus ABCD. If you had to build a fence from point A to C, What is the largest fences you might need to build? Round your answer to the nearest meter.

If the fencing you have to use costs 45 dollars for each meter. What is the most money you might need to spend to build the fence? Round your answer to the nearest dollar.

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9.

Find the value of x.

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10.

Find the value of x.

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11.

Find the value:

x= °

m∠P= °

m∠Q= °

m∠R= °

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12.

List the sides in order from smallest to largest.

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13.

List the sides in order from smallest to largest.

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14.

List the sides in order from smallest to largest.

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15.

List the sides in order from smallest to largest.

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16.

List the sides in order from smallest to largest.

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17.

List the sides in order from smallest to largest.

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18.

List the angles in order from smallest to largest.

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19.

List the angles in order from smallest to largest.

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20.

List the angles in order from smallest to largest.

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21.

List the angles in order from smallest to largest.

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22.

List the angles in order from smallest to largest.

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23.

List the angles in order from smallest to largest.

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24.

List the angles in order from smallest to largest.

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25.

Find the value of x

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26.

Find the value of x

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27.

Find the value of x

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28.

Find the value of x

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29.

Find the value of x

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30.

Find the value of x

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31.

Find the value of x

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32.

Find the value of x

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33.

Find the value of x

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34.

Find the value of x