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Laabri

Chapter 1 Application Review

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G, H, and J are collinear, with H between G and J. Use the given information to write an equation for x, then find GH and HJ:

GH = 5x - 3

HJ = 2x + 7

GJ = 88

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1.

What is the value of x?

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2.

What is the length of GH?

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3.

What is the length of HJ?

S, M, and T are collinear, with M as the midpoint of \overline{ST}. Use the given information to write an equation for x, then find SM and MT:

SM = 9x - 12

MT = 5x + 12

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4.

What is the value of x?

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5.

What is the length of SM?

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6.

What is the length of MT?

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7.

Point P is between W and X. M is the midpoint of \overline{PX}. WX = 32, PM = 7. Using the workspace provided, draw a sketch and find WP.

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8.

Find the distance between the points (-1, 5) and (4, 0). Round your answer to the nearest hundredth.

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9.

Find the midpoint between the points (-12, -8) and (-6, -4).

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10.

Use the given endpoint N(-7, -2) and midpoint M(-3, -6) to find the coordinates of the other endpoint P.

Use the following diagram for the next 2 questions. The locations of Tom's house and Jenny's house are located on the map below.

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11.

Find the midpoint between Tom and Jenny.

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12.

Find the distance between Tom and Jenny. Round your answer to the nearest hundredth.

Use the number line below for the next 4 questions. Find the lengths of each indicated segment.

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13.

BC

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14.

CD

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15.

AC

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16.

DA

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17.

Using the diagram below, what is m\angle{RPT}?

Use the diagram below for the next 2 questions.

\overrightarrow{TY} bisects \angle{WTZ}.

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18.

What is m\angle{YTZ}?

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19.

What is m\angle{WTZ}?

Use the diagram below for the next 3 questions. Use the given information to write an equation for x, then find the measures of \angle{NMU} and \angle{UML}.

m\angle{NMU} = (32x)o

m\angle{UML} = (18x + 1)o

m\angle{NML} = 151o

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20.

What is the value of x?

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21.

What is m\angle{NMU}?

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22.

What is m\angle{UML}?

Use the diagram below for the next 2 questions.

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23.

If m\angle{3} = 46o, then m\angle{1} = ___________

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24.

If m\angle{2} = 156o, then m\angle{4} = ___________

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25.

In the diagram below, m\angle{QPR} = (6x + 8)o and m\angle{SPT} = (7x - 14)o. Solve for x.

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26.

In the diagram below, m\angle{ABD} = (3x + 13)o and m\angle{DBC} = (x + 17)o. Solve for x.

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27.

In the diagram below, m\angle{HKJ} = (7x - 15)o and m\angle{HKL} = (18x - 30)o. Solve for x.

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28.

\angle{7} is supplementary to \angle{8}. m\angle{7} = (x + 3)o and m\angle{8} = (3x + 1)o. Solve for x.

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29.

\angle{5} is complementary to \angle{6}. m\angle{5} = (5x + 3)o and m\angle{6} = (4x + 6)o. Solve for x.

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30.

Using the Pythagorean Theorem to solve for b.

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31.

Using the Pythagorean Theorem to solve for a.

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32.

You are leaning a ladder against a wall. The height of the wall is 12 ft., and the distance from the wall to the foot of the ladder is 3 ft. How long is the ladder? Draw a picture if necessary and use the Pythagorean Theorem.

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33.

You walk 3 miles east, then turn and walk 4 miles north. How far are you, diagonally, from your original location? Draw a picture if necessary and use the Pythagorean Theorem.