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

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Review

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Day 2 2/26/25

Determining Order from Smallest to Largest of Sides of a Triangle

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Determining Order from Smallest to Largest of Angles of a Triangle

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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.

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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 y.

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11.

Find the value:

x= °

m∠P= °

m∠Q= °

m∠R= °

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12.

Match the image with the angle relationship it describes...

Draggable itemarrow_right_altCorresponding Item

arrow_right_alt

Vertical angles

arrow_right_alt

Supplementary angles

arrow_right_alt

Complementary angles

arrow_right_alt

Linear pairs

arrow_right_alt

Adjacent Angles

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13.

Match the definition of the angle relationship with the angle relationships it describes...

Draggable itemarrow_right_altCorresponding Item

Any two angles whose sum is 90°

arrow_right_alt

Vertical angles

Two angles that are

next to each other and

share a common side.

arrow_right_alt

Supplementary angles

Any two angles whose sum is 180°

arrow_right_alt

Complementary angles

Two angles across from each other on

intersecting lines. They are always congruent!

arrow_right_alt

Linear pairs

Two angles that are

adjacent and supplementary.

They form astraight line!

arrow_right_alt

Adjacent Angles

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14.

Match the angle pairs with their relationship.

equal 180 together

are the same size

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15.

Match the example to what type of angle pair it represents.

  • Item 1

  • Item 2

  • Corresponding Angles

  • Alternate Interior Angles

  • Alternate Exterior Angles

  • Same-Side Interior Angles

  • Same-Side Exterior Angles

Key points about parallel lines cut by a transversal (These are your reasons):

Alternate Interior Angles are congruent

Alternate Exterior Angles are congruent

Corresponding Angles are congruent

Same-Side Interior Angles are supplementary

Same-Side Exterior Angles are supplementary

Also

Linear pairs of angles are supplementary

Vertical angles are congruent

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16.

Find x so given that a || b.

x=

What is the reason?

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17.

List the sides in order from smallest to largest.

Smallest

Middle

Largest

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18.

List the sides in order from smallest to largest.

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19.

List the sides in order from smallest to largest.

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20.

List the sides in order from smallest to largest.

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21.

List the sides in order from smallest to largest.

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22.

List the sides in order from smallest to largest.

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23.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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24.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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25.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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26.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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27.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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28.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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29.

List the angles in order from smallest to largest.

Use the "$$ \angle $$" symbol

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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

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35.

Find the value of x

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36.

Find the value of x

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37.

Find the value of x

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38.

Find the value of x

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39.

Find the value of x