Question 1(Multiple Choice Worth 4 points)

Question

(02.04 MC)

What conclusion can be made for c and e?

Triangle ABC has side AB measuring c, side BC measuring 4 units, and angle ACB measuring 36 and a half degrees. Triangle ABC is connected to triangle ACD by shared side AC. Triangle ACD has side AD measuring e and angle ACD measuring 27 and 8 tenths degrees. Segments BC, AC, and DC are marked congruent.

c ≥ e
c ≤ e
c > e
c < e
Question 2(Multiple Choice Worth 4 points)
(02.03 MC)

Angle I = 20 degrees, side HI = 5, angle L = 20 degrees, and side KL = 5. What additional information would you need to prove that ΔHIJ ≅ ΔKLM by SAS?

Angle H is congruent to angle K.
Angle J is congruent to angle M.
Side IJ is congruent to side LM.
Side HJ is congruent to side KM.
Question 3(Multiple Choice Worth 4 points)
(02.04 HC)

C is the centroid of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?

It is given that triangle ABD is isosceles, so segment AB is congruent to DB by the definition of isosceles triangle.
Triangles ABE and DBE share side BE, so it is congruent to itself by the reflexive property.
It is given that C is the centroid of triangle ABD, so segment BE is a perpendicular bisector.
E is a midpoint, creating congruent segments AE and DE, by the definition of midpoint.
Triangles ABE and DBE are congruent by the SSS Postulate.

Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD, segment BC is extended past C with dashed lines so that it intersects with side AD at point E.
There is an error in line 1; segments AB and BC are congruent.
There is an error in line 2; segment BE is not a shared side.
There is an error in line 3; segment BE should be a median.
The proof is correct.
Question 4(Multiple Choice Worth 4 points)
(02.02 MC)

Carlos performed a transformation on trapezoid EFGH to create E′F′G′H′, as shown in the figure below:

A four quadrant coordinate grid is drawn. Trapezoid EFGH with coordinates are drawn at E negative 6, negative 4. F is at negative 4, negative 4. G is at negative 2, negative 6. H is at negative 7, negative 7. Trapezoid E prime F prime G prime H prime with coordinates are drawn at E prime negative 4, 6. F prime is at negative 4, 4. G prime is at negative 6, 2. H prime is at negative 7, 7.

What transformation did Carlos perform to create E′F′G′H′?

Rotation of 270° clockwise about the origin
Reflection across the x-axis
Rotation of 90° clockwise about the origin
Reflection across the line of symmetry of the figure
Question 5(Multiple Choice Worth 4 points)
(02.06 MC)

Look at the quadrilateral shown below:

A quadrilateral ABCD is shown with diagonals AC and BD intersecting in point O. Angle AOB is labeled as 1, angle BOC is labeled as 4, angle COD is labeled as 2, and angle AOD is labeled as 3.

Terra writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

Terra's proof

AO = OC because it is given that diagonals bisect each other.
BO = OD because it is given that diagonals bisect each other.
For triangles AOB and COD, angle 1 is equal to angle 2, as they are ________.
Therefore, the triangles AOB and COD are congruent by SAS postulate.
Similarly, triangles AOD and COB are congruent.
By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC.
As the alternate interior angles are congruent, the opposite sides of quadrilateral ABCD are parallel.
Therefore, ABCD is a parallelogram.

Which is the missing phrase in Terra's proof?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Question 6(Multiple Choice Worth 4 points)
(02.04 MC)

Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 5 in., 5 in., and 2 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?

Yes, according to the Triangle Sum Theorem
Yes, according to the Triangle Inequality Theorem
No, according to the Triangle Sum Theorem
No, according to the Triangle Inequality Theorem
Question 7(Multiple Choice Worth 4 points)
(02.06 MC)

Figure ABCD is a rhombus, and m∠AEB = 7x + 6. Solve for x.

Rhombus ABCD with diagonals AC and BD and point E as the point of intersection of the diagonals.

5.56
12
24.85
Not enough information
Question 8(Multiple Choice Worth 4 points)
(02.01 LC)

Figure EFGHK as shown below is to be transformed to figure E′F′G′H′K′ using the rule (x, y) → (x + 8, y + 5):

Figure EFGHK is drawn on a 4 quadrant coordinate grid with vertices at E 3, negative 4. F is at 5, 1. G is at 3, 5. H is at negative 4, 3. K is at negative 2, negative 3.

Which coordinates will best represent point H′?

(4, 8)
(1, 11)
(12, 8)
(9, 11)
Question 9(Multiple Choice Worth 4 points)
(02.04 MC)

Alex is writing statements to prove that the sum of the measures of interior angles of triangle PQR is equal to 180°. Line m is parallel to line n.

Line n is parallel to line m. Triangle PQR has vertex P on line n and vertices Q and R on line m. Angle QPR is 80 degrees. Segment PQ makes 40 degrees angle with line n and segment PR makes 60 degrees angle with line n.

Which is a true statement he could write?

Angle PRQ measures 40°.
Angle PQR measures 60°.
Angle PRQ measures 80°.
Angle PQR measures 40°.
Question 10(Multiple Choice Worth 4 points)
(02.01 MC)

Triangle XYZ is shown on the coordinate plane.

A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.

If triangle XYZ is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Z″?

(2, −8)
(6, −2)
(8, −2)
(12, −6)
Question 11(Multiple Choice Worth 4 points)
(02.03 MC)

Which of the following would be a line of reflection that would map ABCD onto itself?

Square ABCD with B at 1 comma 3, A at 1 comma 1, D at negative 1 comma 1, and C at negative 1 comma 3.

x = 1
−x + y = 2
x − y = 2
2x + y = 3
Question 12(Multiple Choice Worth 4 points)
(02.03 MC)

Britton rotated trapezoid ABCD 180° on the coordinate plane. If angle B is 20° and angle D is 90°, what is the degree measurement of angle B′?

20°
70°
90°
180°
Question 13(Multiple Choice Worth 4 points)
(02.03 LC)

If ΔSTU ≅ ΔHIJ, then what corresponding parts are congruent?

∠I and ∠U
segment TU and segment HI
∠I and ∠S
segment US and segment JH
Question 14(Multiple Choice Worth 4 points)
(02.03 MC)

A land surveyor places two stakes 500 ft apart and locates the midpoint between the stakes. From the midpoint, he needs to place another stake 100 ft away that is equidistant to the two original stakes. To apply the Perpendicular Bisector Theorem, the land surveyor would need to identify a line that is

perpendicular to the line connecting the two stakes and going through the midpoint of the two stakes
parallel to the line connecting the two stakes and going through the midpoint of the two stakes
perpendicular to the line connecting the two stakes and going through one of the two original stakes
parallel to the line connecting the two stakes and going through one of the two original stakes
Question 15(Multiple Choice Worth 4 points)
(02.01, 02.02 MC)

Triangle XYZ is shown on the coordinate plane.

A triangle on the coordinate plane with vertices X at 5 comma 6, Y at 10 comma 1, and Z at 2 comma 1.

If triangle XYZ is translated using the rule (x, y) → (x + 5, y − 3) and then rotated 90° clockwise to create triangle X″Y″Z″, what is the location of X″?

(−3, 10)
(−2, −15)
(−2, −7)
(3, −10)

Answer 1

Here are the answers to the multiple-choice questions based on the provided information:

Question 1:
What conclusion can be made for c and e?
Answer: c < e

Question 2:
What additional information would you need to prove that ΔHIJ ≅ ΔKLM by SAS?
Answer: Side IJ is congruent to side LM.

Question 3:
Does the following proof correctly justify that triangles ABE and DBE are congruent?
Answer: There is an error in line 3; segment BE should be a median.

Question 4:
What transformation did Carlos perform to create E′F′G′H′?
Answer: Rotation of 270° clockwise about the origin

Question 5:
Which is the missing phrase in Terra's proof?
Answer: vertical angles

Question 6:
Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?
Answer: No, according to the Triangle Inequality Theorem

Question 7:
If m∠AEB = 7x + 6, solve for x.
Answer: Not enough information (since no measurement or equation is provided to solve for x).

Question 8:
Which coordinates will best represent point H′?
Answer: (4, 8) (adding 8 and 5 to the coordinates of H)

Question 9:
Which is a true statement he could write?
Answer: Angle PQR measures 60°.

Question 10:
What is the location of Z″?
Answer: (6, −2)

Question 11:
Which of the following would be a line of reflection that would map ABCD onto itself?
Answer: x = 1

Question 12:
What is the degree measurement of angle B′?
Answer: 20°

Question 13:
If ΔSTU ≅ ΔHIJ, then what corresponding parts are congruent?
Answer: ∠I and ∠U

Question 14:
To identify a line that is:
Answer: perpendicular to the line connecting the two stakes and going through the midpoint of the two stakes

Question 15:
What is the location of X″?
Answer: (−2, −7)

This series of answers corresponds closely with standard geometric and mathematical principles applied to the described scenarios.