Math Final

Which is the best definition of an angle?

An angle is the figure formed by two rays that share the same endpoint

The vertices of triangle ABC are A(-4, 2), B(6, 6), C(2, 7). A translation maps point A to the point A'(6, -3). If B and C are mapped by the same translation, what are the coordinates of B' and C'?

B'(16, 1), C'(12, 2)

Which pair of equations would represent lines that are PERPENDICULAR to each other? I: 3x - 2y =12 II: 3x + 2y = -12 III: 2x - 3y = -12

II and III

Which of the following best describes the construction above?

Ray GE bisects angle FGH

Which equation cannot be used to solve for x in the parallelogram below?

^x+12=7x-8

In the figure below <HFG = <HKJ and HF = HK. Select the triangle congruence criterion that can be used to prove that triangle HFG = triangle HKJ.

angle-side-angle (ASA)

Which equation is parallel to y = -3x + 4 and passes through the point (-3, 4)?

y = -3x - 5

Use the definition of a reflection to answer the following question. The image of point A(2, -6) after a reflection is the point A'. The line of reflection intersects AA' at point (-4,4). What must be the coordinates of A'

(-10,14)

If the triangle ABC is rotated 90 degrees clockwise about the origin, what are the coordinates of B'?

(4, 1 )

The diagram shows triangle QRS. If TU is a midsegment of triangle QRS, what are the coordinates of point U?

(b/2, a/2)

Which transformation represents a rigid motion of a line segment on the coordinate plane?

(x,y) --> (x+a, y+b)

An artist creates a school banner design in the coordinate plane. The artist then reflects this design about a horizontal line. Which functions could represent this reflection? Choose all that apply.

(x,y) --> (x, -y)/(x,y) --> (x,2-y)

Determine the value for b assuming that the two horizontal lines displayed are parallel.

29.00

Claire is constructing a triangular garden, shown below. If Claire would like to completely surround the garden with fencing, how much fencing will she need?

30 ft

A homeowner wishes to put a fence around a space in her yard to create a dog pen. The space that she wants to fence in is shown below where each unit on the graph represents one foot. How many feet of fencing will the homeowner need to build the dog pen?

38 + 10√2

Jennifer needs to use a ladder to clean a seconf floor window on a building. If the windows is 13 ft above the ground and the base of the ladder is 4ft from the building, which equation below can be used to determine the length (x) of the ladder needed to reach the window.

4^2+13^2=x^2

Which is the best definition of a circle

A circle is the set of all points equidistant from a given point.

Kelly is using a compass and straightedge to perform the geometric construction below. Which of the following best describes the figure Kelly is constructing?

A line parallel to RS through Q

Select each statement that is true for all reflections in the coordinate plane.

A point that is mapped to itself after a reflection is on the line of reflection/A line segment connecting a point and its image will be perpendicular to the line of reflection/The distance between a point and its image will be twice the distance between the point and the line of reflection.

Look at the trapezoid shown below. Which Transformation carries the trapezoid onto itself?

A reflection across the line x=-1

On the coordinate plane below, quadrilateral 1 has been transformed to form quadrilateral 2. Which of these could be the transformation? Choose all that are correct.

A reflection across the line x=1/ A translation 2 units to the left, and then a reflection across the y-axis/ A reflection across the y-axis, and then a translation 2 units to the right.

Given AB||DC and <A = <C. Which theorem or postulate can be used to prove triangle ABD = triangle CDB?

AAS

In the figure below, <CAB = <CAD. What additional information would be enough to prove triangle ABC = triangle ADC by the Side-Angle-Side Congruence Postulate?

AB = AD

Joe is asked to prove that the sum of the interior angles (<1,<2, and <3) of the triangle he has drawn equals 180 degrees. His triangle is represented in the diagram above, and his work is shown below. In order for Joe's proof to hold true, which of the following assumptions must be made.

AB II CD

Examine ABC below. Which of the following equations correctly represent the relationship between the segments.

AG = 2GD

The diagram below shows a transversal line crossing through AB and CD. AB is parallel to CD. Given the information above, a student makes the claim <1 = <5. Her work to prove this claim is shown in the table below. Which reason best supports the statement she made in step 3 of her work.

Alternate interior angles formed by two parallel lines are congruent.

Which statements are true for all rotations around the origin? Select all that apply

Angles are taken to angles of the same measure/Circles are taken to circles of the same center and radius/Line segments are taken to the line segments of the same length. Parallel lines are taken to parallel lines

A parallelogram ABCD is shown. Julie is asked to prove that AB=DC and AD=BC. Her proof is shown below. Which reason supports the statement that Julie made in step 6 of her proof.

Corresponding parts of corresponding triangles are congruent.

Figures 1 through 5 are shown below. Select ALL correct sequences of transformations between the indicated figures.

Figure 1 --> Figure 2: A rotation of 180 around the origin, translation of 2 units down and 1 unit right, and a reflection over line x=1/ Figure 1 --> Figure 4: A reflection over line y=2, a second reflection over line x=-2, and a translation of 2 units down/ Figure 5 --> Figure 4: A rotation of 90 counterclockwise about the point (1, -5), followed by a translation of 1 unit up.

Using the diagram, Ginny and Ben both claim they have developed proof that shows that vertical angles are congruent. Their proofs are shown in the table. Which of the following explanations identifies and analyze the proof that supports the correct claim.

Ginny's proof shows that vertical angles are congruent with the use of supplementary angles whose measures have a sum of 180 degrees.

Helga knows that the corresponding angles of two triangles are congruent. She claims that the two triangles must be congruent. Which statement best describes Helga's claim.

Helga is incorrect since the two triangle must also have congruent corresponding sides to be congruent.

Line a is perpendicular to line b, and neither line is vertical. Which statement(s) below are TRUE? I: The slope of line a and line b are the same. II: One line has a positive slope, the other line has a negative slope. III: Line a and line be will never intersect. IV: The slope of one of the lines is undefined

II only

Natasha drew two arcs of the same radius by placing her compass at each endpoint of AB to produce the picture below. If she connects the two points where the arcs intersect with a straightedge, what must be true about the segment she creates.

It is perpendicular to and bisects AB

Lucia draws a square and plots the center of the square. She claims that any rotation about the center of the square that is a multiple of 45 degrees will carry the square onto itself. Which statement best describes Lucia's claim?

Lucia's claim is incorrect since not all rotations that are multiples of 45 degrees carry a square onto itself.

Examine rectangle JKLM, shown below. If JN=x+3 and JL=3x+1, determine which of the following values is correct.

NM=8

On the coordinate plane below, triangle 1 has been transformed using the rule (x, y) --? (-2x, 2y + 2) to create triangle 2. Are triangles 1 and 2 congruent? Why or why not?

No, because each variable is multiplied by a coefficient that is not equal to 1.

Triangles RST and XYZ are shown below. Emma knows that <R = <X and <T = <Z. She claims that triangles RST and XYZ are congruent. As a part of her reasoning, which criterion could she use? Select all that apply.

Side-Angle-Side (SAS)/ Angle-Side-Angle (ASA)

Tessa claim that a rotation of 90 degrees clockwise about the center of some polygons will carry the polygon will carry onto itself. Select TWO polygons that support Tessa's claim.

Square/ Octagon

The diagram below shows the start and finish diagrams of construction using a compass and a straightedge. Which of the following statements are true about this construction? Select all that apply.

The first step of the construction is to draw a circle with center X/The second step fof the construction is to draw the perpendicular bisector of WY

The quadrilateral ABCD is shown below. Julie wants to prove that AC and BD bisect each other. Her proof is shown below. In order for Julie's proof to hold true, which of the following assumptions must be made?

The quadrilateral is a parallelogram

A student claims that a rotation of 180 degrees about the center of a regular polygon carries the polygon carries the polygon onto itself. Which statement best describes the student's claim.

The student claim is true for regular polygons with an even number of sides

Two figures are shown below. Which of the following states correctly explains whether or not the two figures are congruent.

The two figures are congruent since there is a rotation that carries one figure onto the other.

Which statements define a pair of parallel lines, l and m?

The two lines are on the same plane and do not intersect/ The two lines are on a coordinate plane , have different y-intercepts, but have the same slope

Two squares are shown below. Eliza claims that the two squares are congruent. Which statement could be used to prove Eliza's claim?

The two squares are congruent since a translation carries one square onto the other.

Two triangles have corresponding sides that are congruent and corresponding angles that are congruent. Which of the following statements must be true for all such pairs of triangles? Select all that apply.

The two triangle are congruent to each other/ There is a set of rigid motions that carries one triangle onto the other.

Beverly drew the line AB shown below. She then constructed line DC which is the perpendicular bisector of AB. What is true about line segments AD and BD?

They are congruent because the triangles AED and BED are congruent by SAS.

Given AB||DC and AB = DC. Which congruence statement(s) can be proven using the givens and the figure above?

Triangle CAB = triangle ACD only

Which is the best description of a line segment?

Two endpoints connected by a line that represents the shortest distance between the two points

A quadrilateral is drawn on a coordinate plane with vertices at W(-3, 1), X(-1, 5), Y(0, 3), and Z(-2, -1). Andrew wants to prove that the quadrilateral is a parallelogram. Which of the following actions could he take? Select all that apply.

Use the slope formula on each side of the quadrilateral and show that opposite sides have the same slope/ Use the distance formula on each side of the quadrilateral and show the opposite sides have the same length/ Use the midpoint formula on each diagonal of the quadrilateral and show that the diagonals have the same midpoint.

In triangle XYZ, XY=7 inches, YZ=5 inches, and XZ=4 inches. This triangle is reflected across the x-axis to result in triangle X'Y'Z'. Which is the true?

X'Y'=7 inches

In the figure below, points (a, 0) and (0, b) are located on a coordinate plane such that a right triangle is formed along with the axes. Suppose that the perimeter of the triangle is an integral number of units. In that case, which of these are possible values for a and b? Choose all that are correct.

a = 8; b = 15/ a = 24; b = 10/ a = 3; b = 4

Look at the figure below. Select TWO Statements about the figure that are true.

m<TRS=76 degrees/m<WTR=140 degrees

Rectangle WXYZ is shown below. Rectangle WXYZ is rotated by 90 degrees clockwise about vertex X to create rectangle W'X'Y'Z. Based on the definition of rotation, which of the following statements are true? Select all that apply.

m<W'X'W=90 degrees/ m,X'Y'Z = 90 degrees/Y'Z' is parallel to W'X'

The diagram shows triangle MNO. Which of the following must be true if triangle MNO is isosceles with base OM?

p=2r

What type of quadrilateral has the vertices A(3, 6), B(3, 3), C(6, 3), and D(6, 6)?

square

The coordinate plane below shows point P(-2, 2) and the line y=(2/3)x - 1. Which equation describes the line that passes through point P and is perpendicular to the line on the graph.

y=(-3/2)x - 1

On a coordinate plane, triangle FGH is formed with the vertices at point F(0, -2), point G(1, 0), and point H(2, -3). Which expression can be used to determine the perimeter, in units, of triangle FGH?

√(0-1)^2 + (-2, - 0)^2 + √(1-2)^2 + (0-(-3))^2 + √(2-0)^2 + (-3-(-2))^2

On a coordinate plane, the vertices of a quadrilateral are located at these points. R(-4, -4), S(1, 5), T(4, 2), U(-2, 4). What is the perimeter, in units, of the quadrilateral?

√106 +3√2 + 2√10 + 2√17