Review

Review for Mod 1 Test in Geometry

Slope

•  $\frac{rise}{run}$  

• Always count from left to right

•  $Formula:\ \ \ \ m=\frac{y_2-y_1}{x_2-x_1}$ 

Multiple Choice

What is the slope of the following line? (remember to count  $\frac{rise}{run}$  when going  from left to right.)

• $m\ =\ 4$

• $m\ =\ 3$

• $m\ =\ \frac{1}{3}$

• $m\ =\ -3$

Multiple Choice

What is the slope formula?

Multiple Choice

What is the slope of the following line?

• $m\ =-\frac{1}{4}$

• $m\ =\ 4$

• $m\ =\ -4$

• $m\ =\ -\frac{1}{3}$

Multiple Choice

Find the slope given the points (-5,-3) and (2,4).

• 5/4

• 1/7

• -1

• 1

Midpoint

• The point directly between (in the middle of) two points.

• Formula:

   $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$  

• Take the average of the x's and the average of the y's

• Divides the segment into 2 congruent segments

Multiple Choice

Find the midpoint of the line segment with the given endpoints (-2,-6) and (8,8)

• (-4,8)

• (18,22)

• (3,1)

• (-5,-7)

Multiple Choice

Find the midpoint of the segment on the graph. (Hover over picture to expand)

• (2,3)

• (-1,2)

• (5,-3)

• (3,2)

Multiple Choice

Calculate the endpoint given the midpoint (3,4) and

the other endpoint (-1,6).

• (1,5)

• (2,10)

• (7,2)

• (1,2)

Perfect Square List should be memorized so you can simplify radicals

How to Simplify Radicals

• Find the biggest perfect square that will go into the number

• Write the other factor next to it

• Square root the perfect square

Multiple Choice

Simplify the following radical:

 $\sqrt{32}$  

•  $3\sqrt{2}$  
  

•  $4\sqrt{8}$  

•  $16\sqrt{2}$  

•  $4\sqrt{2}$  

How to add and subtract radicals

• You can only combine LIKE radicals

• Simplify your radicals first and look for like radicals

• Only add or subtract the coeffiecients (numbers in front)

Multiple Choice

Add:

 $8\sqrt{5}+\sqrt{5}$  

• 9√5

• 8√10

• 9√10

• 8√5

Parallel Lines cut by a Transversal

• Alternate interior angles are congruent when lines are parallel

• Alternate exterior angles are congruent when lines are parallel

• Corresponding angles are congruent when lines are parallel

• Same-side interior angles are supplementary when lines are parallel

• Check if the angles are acute or obtuse to help you.

Multiple Choice

See Picture

• x = 25

• x = 35

• x = 30

• x = 20

Multiple Choice

Which of the following relationship proves that j is parallel to k?

• ∠3 and ∠4 are supplementary

• ∠4 and ∠5 are supplementary

• ∠1 ≅ ∠3

• ∠2 ≅ ∠3

Multiple Choice

Angles 2 and 8 are

• Corresponding

• Alternate Interior

• Alternate Exterior

• Vertical

Multiple Choice

Name the angle relationship.

• Consecutive Interior

• Alternate Interior

• Corresponding

• Vertical Angles

Multiple Choice

Name the angle relationship.

• Alternate Interior

• Alternate Exterior

• Correpsonding

• Vertical Angles

Multiple Choice

Name the angle relationship.

• Alternate Interior

• Alternate Exterior

• Corresponding

• Vertical Angles

Multiple Choice

Which value of x will show that lines l and m are parallel?

• 20

• 22

• 24

• 25

Multiple Choice

A transversal intersects two lines. Which condition proves that the two lines are parallel?

• Alternate Exterior angles are congruent.

• Same-Side interior angles are congruent

• Vertical angles are congruent.

Rotational Symmetry

• When a figure can be rotated a number of degrees less than 360 and it can look exactly the same.

• Divide 360 degrees by the number of angles or sides the figure has. This is the minimum number of degrees a figure can be rotated to look the same.

• Any multiple of that number also would work.

• Working backwards: You can also divide 360 by the number of degrees to figure out how many sides/angles the polygon has.

Multiple Choice

Which number of degrees below describes an angle that can rotate this regular polygon back onto itself?

• 160

• 320

• 60

• 270

Multiple Choice

Which number of degrees below describes an angle that can rotate this regular polygon back onto itself?

• 45

• 320

• 240

• 90

Multiple Choice

Identify the smallest angle of rotation that maps the image to itself.

• 72°

• 180°

• 144°

• 45°

Translations

 $T_{-5,3}$  means to slide 5 units left      (x-direction) and 3 units up (y direction)

Also written as:
 $\left(x,y\right)\rightarrow\left(x-5,\ y+3\right)$  

Multiple Choice

How is Quadrilateral EFGH translated to E'F'G'H'?

• $\left(x,y\right)\rightarrow\left(x,\ y-6\right)$

• $\left(x,y\right)\rightarrow\left(x+3,\ y+6\right)$
  

• $\left(x,y\right)\rightarrow\left(x-3,\ y-6\right)$
  

Rotations

Every 90 degrees is one-quarter turn.

Pay attention to Clockwise or Counterclockwise

180 degrees is upside down

Multiple Choice

Name the image of C(6, -4) under a rotation 90 degrees clockwise about the origin.

• C'(4, 6)

• C'(-4, -6)

• C'(6, 4)

• C'(-6, -4)

Multiple Choice

The point Z(4, -2) is rotated 180 degrees about the origin.  What is the image of Z?

• Z'(2, 4)
• Z'(-4, 2)
• Z'(-2, -4)
• Z'(-4, -2)

Reflection through a point.

• Count the boxes to the point of reflection, then repeat through it to the other side.

• Example in the picture: The origin is the point of reflection.

• Count down 3 and left 2, repeat again down 3 and left 2 to get to the answer.

• Reflecting through a point is the same as rotating 180 degrees around that point.

Multiple Choice

Point P (3, -7) is reflected through the origin. Therefore, P' is located at:

• (-7, 3)

• (-3, 7)

• (7, -3)

• (0, 0)

Identify which transformation...

These look the same if you look quickly. But look at the letters. The top one is an example of a line reflection, since the letters are flipped. The bottom one is an example of a translation since the image has just been moved over.

PAYATTENTION TO THE LETTERS!

Partitioning a Line Segment

Example:

• Count the slope (rise over run) starting at the left point.

• Divide rise and run by the total number of parts

• Start at the left point, count that number of rise over run.

• Use the first number in the ratio to count to the partitioning point.

Multiple Choice

Given the ratio is 3:1. How many total parts are there?

• 2

• 3

• 4

• 5

Multiple Choice

Given the points A(-2 4) and B(7, -2), find the coordinates of the point P on directed line segment AB in the ratio 1:2.

The coordinates for point P are:

• (0, 1)

• (0, -1)

• (1,2)

• (2,1)

Multiple Choice

What would be the coordinates of point K if it was reflected over the Y-axis?

• (-5, 2)

• (5, 2)

• (5, -2)

Multiple Choice

Is the triangle being reflected in the line x=0 or y=0 ?

• x=0

• y=0

Vertical Angles

• Vertical Angles are always congruent.

• x=x

• y=y

• x+y = 180

Multiple Choice

Find the value of x.

• 14
• 60
• 35
• 180

Line Segment Bisector

• In the image, line k bisects  $\overline{AB}$   

• M is the midpoint.

•  $\overline{AM}\cong\overline{BM}$  

Multiple Choice

B is the midpoint of AC. Find the value of AC. (Hint: Set both halves equal to each other to solve for x, then plug in).

• 2

• 16

• 8

• 4

Angle Bisector

Ray that divides an angle into 2 congruent angles. 

 $\overrightarrow{KM}$  bisects  $\angle LKJ$  so that  $\angle LKM\cong\angle JKM$  

The two smaller angles formed must be equal in measure to each other.
Two times a smaller angle = the whole big angle.

Multiple Choice

The angle is bisected. Solve for x. (Hint: Set both halves equal to each other to solve for x).

• 2

• 3

• 4

• 5

• 7.4

Multiple Choice

Find the value of x if BD is an angle bisector.

• x=67

• x=43

• x=55

• x=12

Multiple Choice

 $\overrightarrow{BD}$  bisects $\angle ABC$ ,  $m\angle ABD=3x+5$  and  $m\angle ABC=2x+30.$ Find  $m\angle DBC.$  DRAW THIS OUT.

•  $15\degree$  

•  $35\degree$  

•  $5\degree$  

•  $20\degree$  

Given a ratio of 3 angles of a triangle: such as 1:3:8

Put an x after each number, and all up all 3 angles to equal 180 degrees. Solve for x, then plug it in to find each angle or the desired angle.

Multiple Choice

The angles of a triangle are in the ratio of 2:3:4. What is the measure of the smallest angle?

•  $20\degree$  

•  $40\degree$  

•  $80\degree$  

Multiple Choice

Which angles are vertical angles?

• $\angle8\ \&\ \angle7$

• $\angle8\ \&\ \angle6$

• $\angle8\ \&\ \angle5$

Isosceles Triangles have 2 congruent sides and 2 congruent angles across from them. The angle that is different is called the vertex angle.

Equilateral triangles have all sides congruent and all angles congruent. Each angle in an equilateral triangle measures  $60\degree.$  

Multiple Choice

Solve for x. (remember this triangle has 2 congruent sides AND 2 congruent angles).

• x = 118

• x = 31

• x = 23

• x = 62

Multiple Choice

Solve for x. (Hint: This triangle is equilateral! So all sides and angles are congruent.)

• 60

• 48

• 30

• 28