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100

The lengths of two sides of △PQR and QR and PR, are 12 cm and 5 cm. Which measurement is in the range of possible side lengths for PQ?

6 cm

7 cm

15 cm

17 cm

  

15 cm

100

In the figure below, line a || line b.



If m∠2 = 78°, which of the following angles also measure 78°? Select THREE that apply.

  • ∠3

  • ∠4

  • ∠5

  • ∠6

  • ∠7

  • ∠8

∠4

∠6

∠8

100

one side of a triangle is 9cm and the another 13cm

Emma and Malik claim the following about the third side

Emma: The length of the third side of the triangle must be in the range 9<s<13cm.
Malik: The length of the third side of the triangle must be in the range 4<s<22 cm.

Which statement about Emma’s and Malik’s claims is correct?

  • Only Emma’s claim is correct.

  • Only Malik’s claim is correct.

  • Both Emma’s and Malik’s claims are correct.

  • Neither Emma’s nor Malik’s claim is correct.

only Malik's claim is correct

100


In the diagram below Points G, H, and I are collinear.

Which conjecture is not necessarily true?

  • a  ∠GHK≅∠KHI

  • b  m∠GHJ+m∠JHI=180 °

  • c   ∠ G H J and ∠ J H I form a linear pair
  • d   ∠ G H K and ∠ J H I are vertical angles



Correct Answer


  • d   ∠ G H K and ∠ J H I are vertical angles
100

Which counterexample can be used to show that the following conjecture is false?

Given:          ∠1 and ∠2 are adjacent angles.
Conjecture: ∠1 and ∠2 are supplementary angles.


a



  • b
  • c

  • d

d

200

A drawing of a wagon wheel with evenly spaced spokes is shown below.

What is the value of x?



Responses

  • 30°

  • 45°

  • 60°

  • 90°

45

200

In the street map shown, Adams Street, Becker Street, and Cabell Street form a triangle. Dunlop Street connects the intersection of Adams and Becker Streets with Cabell Street. Erving Street connects the intersection of Becker and Cabell Streets with Adams Street.

Which two streets intersect to form an angle with a measure of 28°?



  • Adams and Dunlop

  • Adams and Becker

  • Becker and Dunlop

  • Cabell and Erving

Becker and Dunlop

200

A section of a leaded glass window is shown below.

Given:
     • Each piece of lead in the glass is a straight line segment.
     • ∠1≅∠2
     • ∠1≅∠3

Which justification proves that ∠2≅∠3?



Responses

  • addition property

  • transitive property

  • vertical angles are congruent

  • alternate interior angles are congruent

transitive property

200

What conclusion would be true given the hypothesis “If Angle 1 is congruent to Angle 2, and Angle 2 is congruent to Angle 3, then . . .”?



  • the measure of Angle 1 is greater than Angle 3.

  • the measure of Angle 1 is less than Angle 3.

  • Angle 1 is supplementary to Angle 3.

  • Angle 1 is congruent to Angle 3.

Angle 1 is congruent to Angle 3.

200

Two poles represented by AB¯ and CD¯ are bolted together at E. Pole AB¯ makes an angle of 78° with the ground, and pole CD¯ makes an angle of 81° with the ground.

What is the measure of ∠DEB?


19°

21°

22°

25°

21

300

A floor is being covered with regular hexagonal tiles. A tile must be cut in half, as shown, to fit against a wall.

What is the measure of angle P in the cut tiles?



  • 45º

  • 60º

  • 90º

  • 120º

60

300

Marisa is building a bookstand with a triangular base. If two angles of the triangular base measure 75° and 35°, what is the measure of the third angle?

  • 50°

  • 60°

  • 70°

  • 80°

70

300

A stop sign is a regular octagon with eight congruent sides and eight congruent angles. What is the sum of the measures of the interior angles?



  • 780º

  • 900º

  • 1080º

  • 1260º

1080

300

Consider rectangle RSTU.

What is the length of VS?

a  5.4

b  5.9

c  6.2

d  6.5

d  6.5

300

Which statement requires additional information to prove that a quadrilateral is a parallelogram?


  • The diagonals of the quadrilateral bisect each other.

  • One pair of opposite sides of the quadrilateral is parallel..

  • Both pairs of opposite angles of the quadrilateral are congruent.

  • One pair of opposite sides of the quadrilateral is both parallel and congruent.

One pair of opposite sides of the quadrilateral is parallel..

400

Which inequality regarding the side lengths of △ABC is true?



Responses

  • AC<AB<BC
  • AB<AC<BC
  • BC<AB<AC
  • AB<BC<AC


AC<AB<BC

400

Which inequality correctly compares the sides of △ABC



Responses

  • BC<AB

  • AC<AB
  • AC<BC
  • BC<AC


  • BC<AC
400

A new perfume was sold in a package shaped like the square pyramid shown below.

What is the sum of the angles of the faces, including the base, of the perfume package?

a  720

b  1800

c  1080

d  900



b 1080

400

The diagram below shows rectangle RSTU with two diagonals drawn.

 

To find the value of x, Justin wrote the following steps.

1. m∠STR+m∠RTU=90
2. m∠RTU=27°
3. 6x−15=27
4. 6x=42
5. x=7

Which statement can be used to justify the first step?



Responses

  • The alternate interior angles formed by the diagonals are congruent.

  • The angles at each vertex of the rectangle are right angles.

  • Opposite angles in a rectangle are congruent.

  • The diagonals of a rectangle are congruent.

The angles at each vertex of the rectangle are right angles.

400

Given: In Quadrilateral ACDE, ∠EAB≅∠EBA, AE ≅CD and BC≅DE.
Prove: BCDE is a parallelogram.

STATEMENTS                                                              REASONS 

1. ∠EAB≅∠EBA                                        Given
   
2. AE≅BE    2. Converse of the isosceles triangle
                                                                 
3. BE≅CD                      3. Substitution Property
4. BCDE is a parallelogram                       4. ? 

Which statement can be used to justify Step 4 in this proof?

  • If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

  • If both pairs of opposite angles in a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  • If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

500

Clarissa is writing a proof to show that the diagonals of a parallelogram bisect each other. She is using the figure below.

Which of the following statements should be used in Clarissa’s proof?

  • ∠DEC≅∠BEA

  • LineAB ∥  LineCD

  • AE=EC

  • AE+ED=BE+EC


LineAB ∥  LineCD

500

The following information is given about a trapezoid: A trapezoid is isosceles if its non-parallel sides are congruent. Trapezoid ABCD is not isosceles. Based on the information, which statement is a valid conclusion about Trapezoid ABCD?



  • The parallel bases are congruent.

  • The non-parallel sides are perpendicular.

  • The non-parallel sides are not congruent.

  • One base and one non-parallel side are perpendicular.

The non-parallel sides are not congruent.

500

Examine ΔABC below.



Determine which of the following relationships are true.  Select all that apply.


  • a  DE = 2AC

  • b  m∠BCA = 2(m∠BED)

  • c  DE || AC

  • d  m∠BAC = m∠BCA

c  DE || AC

500

Standing at Point P on Earth where O represents the center, an explorer seeks to determine his latitude (∠EOP) by measuring ∠APB (the inclination of the North Star above the horizon).

Given that PB⊥OE,∠APO=∠90°, and that ∠APB= 40°, what is the measure of ∠EOP ?


  • 30°

  • 40°

  • 50°

  • 60°

40

500

Consider quadrilateral ABCD shown in the diagram.

Which of the following is true if and only if ABCD is a parallelogram?

  • a  ∠ACD≅∠CAD and ∠BAC≅∠BCA

  • b  ∠ACD≅∠BAC and ∠BCA ≅ ∠CAD

  • c  m∠ADC + m∠BAC = 90°

  • d  m∠CAD+m∠ADC+m∠ACD=180°



b  ∠ACD≅∠BAC and ∠BCA ≅ ∠CAD.