Question 1

The Euclidean Geometry mathematical system is an axiomatic system. The axiomatic validation process for theorems is based on logical and deductive thinking methods. Vincent created the following diagram to illustrate the validation process. Which of the following descriptions best supports Vincent's diagram?

Question 2

The Egyptians knew about the Pythagorean Theorem and used a rope with equally spaced knots to mark out right angles and to measure distances. The Egyptians used this method to build magnificent structures like the Pyramids at Giza. Which of the following diagrams could represent the Egyptians' 12-knot rope tool?

A.	C.
B.	D.

Question 4

A geometric construction of a line, b, perpendicular to a given line, a, through point A can be created using a straight edge and a compass. Which of the following diagrams shows the correct way to construct line b?

A.	C.
B.	D.

Question 5

Laura Numeroff wrote If you Give a Mouse a Cookie, a children's book containing a string of conditional statements. The book begins as follows:

If you give a mouse a cookie, He's going to ask for a glass of milk. When you give him the milk, He'll probably ask you for a straw.

Which of the following is true regarding the two conditional statements in this excerpt?

1. The contrapositive of the first statement is: If you don't give a mouse a cookie, then he won't ask for a glass of milk.
   The contrapositive of the second statement is: If the mouse doesn't ask for a straw, then you won't give him the milk.


2. The converse of the first statement is: If the mouse asks for a glass of milk, then you'll give him a cookie.
   The converse of the second statement is: If the mouse asks for a straw, then you'll give him the milk.


3. The inverse of the first statement is: If you don't give a mouse a cookie, then he won't ask for a glass of milk.
   The inverse of the second statement is: If you give the mouse a glass of milk, then he'll ask you for a straw.


4. The converse of the first statement is: If the mouse asks for a glass of milk, then you'll give him the milk.
   The converse of the second statement is: If the mouse asks for a straw, you'll give him a cookie.

Question 6

The Pythagorean Theorem states: In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

The converse of the Pythagorean Theorem is also true. Which of the following is the converse of the Pythagorean Theorem?

Question 7

Mr. Havishaw drew line segment AB intersected by lines b and c. The measure of∠5 is 85 ° and the measure of ∠4 is 90 °. Which of the following conclusions and reasoning would be most appropriate?

1. Lines b and c will intersect because m∠4 + m∠5 = 180 °.


2. Lines b and c are parallel because m∠4 + m∠5.


3. Lines b and c are parallel because m∠1 = m∠3 = m∠6 = m∠8 = 90°


4. Lines b and c will intersect because m∠4 + m∠5 < 180 °.

Question 8

Derick sketched the following rectangular prism with line in the top plane of the figure and line in the bottom plane of the figure. Which of the following conjectures is true?

1. and are parallel because they do not intersect.


2. and are skew because they are not coplanar and do not intersect.


3. and are line segments and do not intersect.


4. and are skew because they are coplanar and do not intersect.

Question 9

Maddie drew a regular polygon with 14 diagonals (line segments that connect two nonconsecutive vertices). She labeled the polygon as a heptagon. Which of the following supports Maddie's conclusion?

1. A heptagon has 7 sides and 14 diagonals because n(n − 3) 2 = 7(7 − 3) 2 = 7(4) 2 = 14


2. A heptagon has 7 sides and 28 diagonals because n(n − 3) = 7(7 − 3) = 7(4) = 28


3. A heptagon has 14 sides and 77 diagonals because n(n − 3) 2 = 14(14 − 3) 2 = 14(11) 2 = 77


4. A heptagon has 7 sides and 7 diagonals because n(n − 2) 5 = 7(7 − 2) 5 = 7(5) 5 = 7

Question 10

The circle below is divided into 6 equal segments. Which of the following statements about circle A is false?

1. measure of arc BC = measure of arc DE = 60°


2. measure of arc BD = measure of arc GH = 60°


3. measure of arc BE = measure of arc DH


4. measure of arc BC = measure of arc CD = 60°

Question 12

On the map below, Carter Street intersects Avenue A and Avenue B, which are parallel. Avenue B, Carter Street, and a sidewalk border the playground. Which of the following lists could represent the angles of the playground?

1. 30°, 60°, 90°


2. 20°, 60°, 90°


3. 30°, 30°, 120°


4. 30°, 60°, 60°

Question 13

In the diagram below, lines a, b, and c, intersect at point P. Which of the following statements is false?

1. m∠2 + m∠3 + m∠4 = 180°


2. m∠3 + m∠4 + m∠5 = 90°


3. m∠1 + m∠2 + m∠3 = 180°


4. m∠3 = m∠6

Question 15

Natalie drew three right triangles and measured their sides using three different units. Four of Natalie's friends made conjectures about the triangles.

• John: The length of the hypotenuse of a right triangle is always equal to the sum of the length of the other two sides.


• Sophia: The perimeter of a right triangle is greater than the sum of the length of the three sides.


• Robbie: The square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.


• Mia: The square of the length of the hypotenuse is equal to the difference of the squares of the other two sides.

Which of Natalie's friends is always correct?

Question 16

Select the conditional statement that is a correct interpretation of the Venn diagram below.

Question 17

Andrew is flying a kite in his back yard. The kite string is 26 feet long and the shadow of the kite is 24 feet away. Which of the following diagrams could Andrew use to determine the height of the kite?

A.	C.
B.	D.

Question 18

Parallel lines behave differently in hyperbolic, spherical, and planar surfaces. Label each of the following sets (A, B, C) of parallel lines as hyperbolic, spherical, or planar.

Question 19

A familiar children's song, If You're Happy and You Know It contains the following line:

If you're happy and you know it, then your face will surely show it

Which of the following is true regarding the conditional statements from this song?

Question 20

Given circles A and C, the radii, AB and, CD are congruent. Which of the following statements is true about circles A and C?

1. Circle A and circle C are colinear.


2. Circle A and C are tangent.


3. Circle A and circle C are concentric.


4. Circle A and circle C are congruent.

Question 21

A geometric construction is shown below. Which of the following is a true statement about this construction?

Question 22

Plane A and Plane B intersect. Which of the following could represent the intersection of the two planes?

Quesiton 23

Mrs. Vincent asked four students to draw angles R and S, a pair of adjacent angles, on the board. Their sketches are below. Which student correctly drew the pair of adjacent angles?

Isabelle	Ricky
Elizabeth	Jacob

Question 25

Xavier created the figure below using a set of geometric puzzle pieces. Which of the following methods could Xavier use to find the total area of the puzzle pieces?