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Laabri

6.4 Geometry Basics (Due 3/12/24)

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Part 2: Finding Measures of Angles with a Protractor

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Part 3 : Using Algebra

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Essential Question: What are the fundamental concepts of Geometry?

Learning Target: Students will be able to demonstrate understanding and give examples of the fundamental concepts of Geometry using their own examples.

Complete the entire assignment and show work for full credit.

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1.

What type of angle is formed by a straight line?

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2.

What is an angle between 90 and 180 degrees called?

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3.

What type of angle measures between 0 and 90 degrees?

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4.

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

Draggable itemarrow_right_altCorresponding Item

Two angles that are

adjacent and supplementary.

They form astraight line!

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Vertical angles

Two angles that share a vertex and

a common side. They are next to each other

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Supplementary angles

Two angles across from each other on

intersecting lines. They share a vertex and they are always congruent!

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Complementary angles

Any two angles whose sum is 180°

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Linear pairs

Any two angles whose sum is 90°

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Adjacent Angles

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5.

Select all the adjacent angles to ∠1

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6.

Select all the vertical angles to ∠1

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7.

Select all the adjacent angles to ∠7

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8.

Select all the supplemental angles to ∠1

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9.

Select all the vertical angles to ∠7

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20.
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21.
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22.

If m∠UVX= 76 and m∠XVW= 64, what is the measure of m∠UVW?

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23.

If m∠GHJ= 27 and m∠GHK= 87, what is the measure of m∠JHK?

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24.
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25.

If m∠PQT =109° and m∠SQR = (4x – 15)°, find the value of x.

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26.

If m∠PQT =109° what is the measure of m∠TQR?

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27.
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28.

What is the correct order of steps to solve this problem?

  1. Divide both sides of the equation by 3

  2. Make 3x+47 equal to 6x-25; because vertical angles are equal

  3. 6(24)-25=119; therefore the m∠SQR=119°

  4. x=24

  5. Substitute 24 for x into 6x-25 to find out what the m∠SQR equals

  6. Add 25 to both sides of the equation

  7. Subtract 3x from both sides of the equation

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29.

What is the m∠SQR=?

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30.

If m∠DEG = (5x – 4)°, m∠GEF = (7x – 8)°, m∠DEH = (9y + 5)°, find the value of x.

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31.

Use the answer from the previous problem to find the measure of ∠GEF.

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32.

Use the answer from the previous problem.

If m∠DEG = (5x – 4)°, m∠GEF = (7x – 8)°, m∠DEH = (9y + 5)°, find the value of y.