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These questions are to help you be prepared for the short answer questions on the unit test. Please make sure that you know how to complete them and have the material in your notes.

Question 1
Which of the following are properties of all rhombus? Check ALL that apply(3 points)
Responses

The diagonals bisect each other at a 90 degree angle
The diagonals bisect each other at a 90 degree angle

All angles are 90 degrees
All angles are 90 degrees

Opposite angles are equal
Opposite angles are equal

All four sides are equal length
All four sides are equal length

The diagonals are congruent
The diagonals are congruent
Question 2
In the picture below, AG = GB

If AG = 7x+9 and GB = 12x - 6, find the length of AB

(1 point)
AB=

Question 3
For the picture below FG ¯¯¯¯¯¯¯¯¯
is a perpendicular bisector of AB¯¯¯¯¯¯¯¯
. Which points are equidistant from points A and B? Check ALL that apply

(4 points)
Responses

Y
Y

X
X

S
S

F
F

Z
Z

W
W

P
P

G
G
Question 4
Which theorem proves this?(1 point)
Responses

Perpendicular Bisector Theorem
Perpendicular Bisector Theorem

Triangle Sum Theorem
Triangle Sum Theorem

Vertical Angles theorem
Vertical Angles theorem

Converse of Alternate Interior Angles Theorem
Converse of Alternate Interior Angles Theorem
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1 answer

Let's tackle each question one by one:

Question 1: Properties of a Rhombus The properties of all rhombuses include:

  1. The diagonals bisect each other at a 90-degree angle. ✔️
  2. Opposite angles are equal. ✔️
  3. All four sides are equal length. ✔️

So the correct responses are:

  • The diagonals bisect each other at a 90 degree angle
  • Opposite angles are equal
  • All four sides are equal length

Note: All angles being 90 degrees is a property of a square, which is a specific type of rhombus, not all rhombuses.

Question 2: Finding Length of AB Given:

  • AG = 7x + 9
  • GB = 12x - 6

Since AG = GB, we set the two equations equal to each other: \[ 7x + 9 = 12x - 6 \]

Now, let's solve for x:

  1. Rearranging gives us: \[ 9 + 6 = 12x - 7x \] \[ 15 = 5x \] \[ x = 3 \]

Now substitute x back into either AG or GB to find the length of AB: \[ AG = 7(3) + 9 = 21 + 9 = 30 \] \[ GB = 12(3) - 6 = 36 - 6 = 30 \]

Since AB = AG + GB = 30 + 30, we find: \[ AB = 60 \]

Thus, AB = 60.

Question 3: Points Equidistant from A and B Since FG is the perpendicular bisector of AB, any point on the line FG is equidistant from A and B. Therefore:

  • Y
  • X
  • S
  • F (since it's on the line)
  • Z
  • W
  • P
  • G (since it's on the line)

All points (Y, X, S, F, Z, W, P, G) are equidistant from points A and B.

Question 4: Theorem that Proves the Situation The correct theorem that applies to the scenario where FG is a perpendicular bisector of AB is the Perpendicular Bisector Theorem. This theorem states that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Therefore, the answer is:

  • Perpendicular Bisector Theorem

Feel free to ask if you need any additional explanations or help!