Study for Geometry

Given R, S, and T are colinear with S between R and T. If RS = 24, ST = 3x – 4, and RT = 5x - 12, find the value of x. Then find RT. (Hint: do this on paper!)

• x=16 rt=-7

• x=16 rt=68

• x=1 rt=-7

• x=1 rt=68

Given F, G, and H are collinear with G between F and H. Find the value of x, if FG = 3x + 1, GH = 2x – 2, and FH = 64. Then find FG and GH. (Hint: figure it out on paper)

• x=12.6 fg=23.2 gh=38.8

• x=12.6 fg= 38.8 gh=23.2

• x=13 fg=24 gh=40

• x=13 fg=40 gh=24

Point H is in the interior of ∠EFG. Find the m∠EFH if m∠HFG=63 and m∠EFG=127. (Hint: easier than you may think. Draw it on paper.)

• 190

• 64

• 126

• 127

If mABC=6x-3, mCBD=4x+2 and mABD=79, then find x and the mCBD.

• x=8 MBC=34 mCBD=45

• x=8 mABC=45 mCBD=34

• x=7.8 mABC= 43.8 mCBD=33.2

• x=7.8 mABC= 33.2 mCBD=43.8

The coordinates of point T are ​(0​,3​). The midpoint of ST is ​(5​,−2​). Find the coordinates of point S.

• (7,-10)

• (-7,10)

• (10,-7)

• (-10,7)

Find the midpoint of the line segment joining points A and B.

A(6,−5)​ ; B(4,1)

• (5,-2)

• (-5,2)

• (-2,5)

• (2,-5)

How far would you travel from Platform B to Platform​ C, if you were on a zipline? Remember: Formula is

 $d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$  

(a)  

Write a​ two-column proof of the Linear Pairs Theorem.

If ​∠ABC and ​∠CBD are a linear​ pair, then ​∠ABC and ​∠CBD are supplementary.

• 1-Given 2-addition theorem 3-linear pairs theorem

• 1-Given 2-Definition of supplementary angles 3-Linear Pairs Theorem

• 1-Given 2-Linear Pairs Theorem 3-Definition of supplementary angles

• 1-Given 2-linear pairs theorem 3- addition theorem

Jacy was asked to write the following statement as a conditional. Water freezes if it is below 0°C. She​ wrote, "If water​ freezes, then it is below 0°​C." What error did she​ make? What is the correct​ conditional?

• She reversed the hypothesis and the conclusion. The correct conditional is "if water is below 0°C, then it freezes."

• She did not recognize that the given statement included​ "if" and​ was, therefore, already a conditional.

• She reversed the hypothesis and the conclusion and did not negate them. The correct conditional is​ "If water is not below 0°​C, then it does not​ freeze."

• She did not negate the hypothesis and the conclusion. The correct conditional is​ "If water does not​ freeze, then it is not below 0°​C."

Emma found a counterexample to a given conditional. What are the truth values of the hypothesis and the​ conclusion? Explain.

The condition must be (a)   for Emma's counterexample.