Practice Test

Match the formula in the picture to one the following: a. Pythagorean Theorem b. Distance Formula in the Coordinate Plane c. Midpoint of a Segment in the Coordinate Plane d. Distance Formula on a Number Line e. Midpoint of a Segment on a Number Line

b

Use the translation (x,y)->(x-5,y+8). What is the image of B(4,2)?

(-1,10)

Use the translation (x,y)->(x-5,y+8) What is the image of J(0,2)?

(-5,10)

Find the coordinates of the midpoint of a segment having the given endpoints: M(11,-2), N(-9,13)

(1,5.5)

Use the translation (x,y)->(x-5,y+8) What is the preimage of F'(-3,-4)?

(2,-12)

Find the coordinates of the midpoint of a segment having the given endpoints: A(0,0), B(12,8)

(6,4)

Find the coordinates of the midpoint of a segment having the given endpoints: S(10,-22), T(9,10)

(9.5,-6)

Always, sometimes, never: Parallel lines are ______________________ the same distance apart.

always

Match the formula in the picture to one the following: a. Pythagorean Theorem b. DIstance Formula in the Coordinate Plane c. Midpoint of a Segment in the Coordinate Plane d. Distance Formula on a Number Line e. Midpoint of a Segment on a Number Line

e

Determine if each conjecture is true or false. Conjecture: every pair of supplementary angles includes an obtuse angle

false

Determine if each conjecture is true or false. Given: AB+BC=AC Conjecture: AB=BC

false

True or False: Perpendicular lines can be formed by intersecting or nonintersecting lines

false

True or False: Transversals must always be parallel

false

True or False: Points W, X, Y, and Z are coplanar

false

There is exactly one ..... through any two points.

line

Always, sometimes, never: Parallel lines _____________________ intersect.

never

Determine whether the following statements is always, sometimes, or never true. Two lines can intersect at two points.

never

Points that do not lie in the same plane are called...

non-coplanar points

There is exactly one ..... through anny three non-collinear points.

plane

Always, sometimes, never: Parallel lines are ______________ cut by a transversal.

sometimes

Always, sometimes, never: Parallel lines that are cut by a transversal ________________ form right angles.

sometimes

Determine whether the following statements is always, sometimes, or never true. A transversal passes through two parallel lines.

sometimes

Determine whether the following statements is always, sometimes, or never true. There is exactly one plane that contains any three points.

sometimes

Use the distance formula to find the distance between A(0,0) and B(15,20)

25

Find the slope of the line given the information: The line goes through (6,2) and (1,7)

-1

Find the slope of the line given the information: The line that is parallel to 3x+2y=12

-1.5

Find the slope of the line given the information: The line that's perpendicular to y=-3x-1

1/3

Make a diagram. Points P, Q, R, S, and T are all collinear. If PR=RT, S is the midpoint of RT, QR=4, and ST=5, complete the sentence: RT=

10

Make a diagram. Points P, Q, R, S, and T are all collinear. If PR=RT, S is the midpoint of RT, QR=4, and ST=5, complete the sentence: PR=

10

Make a diagram. Points P, Q, R, S, and T are all collinear. If PR=RT, S is the midpoint of RT, QR=4, and ST=5, complete the sentence: RS=

5

Make a diagram. Points P, Q, R, S, and T are all collinear. If PR=RT, S is the midpoint of RT, QR=4, and ST=5, complete the sentence: PQ=

6

The measure of the smallest angle of a right triangle is 27 degrees. What is the measure of the second to smallest angle?

63 degrees

Two angles are supplementary. One angle measures 15° less than the other one. Find the measure of the two angles.

97.5°, 82.5°

Name a property that justifies this statement. If AB=CD, then ½AB=½CD.

Multiplication Property of Equality

Are triangles A(1,7), B(2,8), C(3,7) and D(2.5, 17.5), E(5,20), F(7.5, 17.5) congruent? Describe the transformation that supports your answer.

No; ABCis mapped to DEF by a dilation with a scale factor that doesn't equal 1: (x,y)->(2.5x, 2.5y)

Write each statement as a conditional statement. Identify the hypothesis and conclusion. Write the converse, inverse, and contrapositive of the original conditional statement. A man that is six feet tall can wrestle a crocodile.

Original: If a man is six feet tall, then he can wrestle a crocodile. Hypothesis: A man is six feet tall Conclusion: He can wrestle a crocodile Converse: If a man can wrestle a crocodile, then he is six feet tall. Inverse: If a man is not six feet tall, then he cannot wrestle a crocodile. Contrapositive: If a man cannot wrestle a crocodile, then he is not six feet tall.

Write each statement as a conditional statement. Identify the hypothesis and conclusion. Write the converse, inverse, and contrapositive of the original conditional statement. An acute angle has a measure less than 90 degrees.

Original: If an angle is acute, then it's measure is less than 90 degrees. Hypothesis: An angle is acute Conclusion: It's measure is less than 90 degrees Converse: If an angle's measure is less than 90 degrees, then it is acute. Inverse: If an angle is not acute, then it's measure is not less than 90 degrees. Contrapositive: If an angle's measure is not less than 90 degrees, then it is not acute.

Name a property that justifies this statement. If m<1=90 and m<1=m<2, then m<2=90.

Substitution Property of Equality

Name a property that justifies this statement. If m<1=m<2, then m<2=m<1

Symmetric Property of Equality

Identify and describe the transformation: M: (x,y)->(x+4,y-6)

This is a translation four units right and six units down.

Match the formula in the picture to one the following: a. Pythagorean Theorem b. DIstance Formula in the Coordinate Plane c. Midpoint of a Segment in the Coordinate Plane d. Distance Formula on a Number Line e. Midpoint of a Segment on a Number Line

a

Which conditional statement can be used to write a true biconditional? a. If a figure is square, then it is a rectangle. b. If the product is odd, then both factors are odd. c. If two angles form a linear pair, then they are both adjacent. d.If two angles are supplementary, then both angles are obtuse.

b

Match the formula in the picture to one the following: a. Pythagorean Theorem b. DIstance Formula in the Coordinate Plane c. Midpoint of a Segment in the Coordinate Plane d. Distance Formula on a Number Line e. Midpoint of a Segment on a Number Line

c

Points that lie on the same line are called...

collinear points

What is a valid conclusion to the following hypothesis? If there are two points....

there is only one line containing both points

True or False: Perpendicular lines always form multiple right angles

true

True or False: Points X and Z are collinear

true

<1=<3. m<1=70-x and m<3=6x. Find x and the measure of each angle.

x=10, <1=60°, <3=60°

If the line r through (4,4) and (6,2) is perpendicular to line s through (x,-1) and (4,y), what are possible values for x and y?

x=2, y=1

E is the midpoint of DF. Find the value of x. DE=3x, EF=x+6

x=3

E is the midpoint of DF. Find the value of x. DE=5x+3, EF=33

x=6

E is the midpoint of DF. Find the value of x. DE=2x-3, EF=5x-24

x=7

Write the equation of the line: The line perpendicular to y=3x-1 and through (12,15)

y=-1/3x+19

Write the equation of the line: The line through (6,2) and (1,7)

y=-x+8

Write the equation of the line: The line parallel to y=2x-6 and through (0,0)

y=2x