1.
Find the area of the figure below:
2.
Find the perimeter to the nearest tenth.
Explanation
The given answer of 17.3 units is the correct perimeter. Since the question asks for the perimeter to the nearest tenth, it implies that the units are already in place. Therefore, the answer remains as 17.3 units.
3.
Which of the following are true?
Correct Answer
A. Lines AE, BE, CE and DE are concurrent at point E.
Explanation
The correct answer is that lines AE, BE, CE, and DE are concurrent at point E. This means that all four lines intersect at the same point, E. This can be visualized as a point where all four lines meet. The other statements are not true. Points A, E, and D are collinear, meaning they lie on the same line. Points A, E, and D are also coplanar, meaning they lie on the same plane. Lines AB, AE, and CD are not concurrent at point A, as they do not intersect at the same point. Therefore, the correct answer is that lines AE, BE, CE, and DE are concurrent at point E.
4.
A tetrahedron has 4 triangular faces. How many edges does it have?
Correct Answer
6
Explanation
A tetrahedron is a three-dimensional geometric shape with four triangular faces. Each triangular face shares an edge with two other faces. Therefore, each edge of the tetrahedron is shared by two triangular faces. Since each triangular face has three edges, the total number of edges in a tetrahedron is 3 multiplied by the number of triangular faces, which is 3 multiplied by 4, equaling 12. However, each edge is counted twice in this calculation, so we divide the total by 2 to get the actual number of unique edges, which is 6.
5.
How many distinct planes does the tetrahedron's faces define?
Correct Answer
4
Explanation
A tetrahedron is a three-dimensional shape with four triangular faces. Each face of the tetrahedron defines a distinct plane, as no two faces lie in the same plane. Therefore, the tetrahedron's faces define four distinct planes.
6.
How many corners does the tetrahedron have?
Correct Answer
4
Explanation
A tetrahedron is a three-dimensional geometric shape that consists of four triangular faces. Each face of the tetrahedron has three corners, and since there are four faces, the tetrahedron has a total of four corners.
7.
What is true based on the Euler diagram shown below?
Correct Answer
D. If you get a lot of sleep, then you do not have a newborn child.
Explanation
Based on the Euler diagram shown, the correct answer is that if you get a lot of sleep, then you do not have a newborn child. This is because the diagram shows that the circle representing "getting a lot of sleep" is completely outside the circle representing "having a newborn child." Therefore, there is no overlap between the two circles, indicating that these two conditions are mutually exclusive.
8.
What vocabulary word describes the two statements below?If you wear blue, then you are a senior.If you are a senior, then you wear blue.The second statement is the _____________ of the first statement.
Correct Answer
converse
Explanation
The term "converse" is used to describe the second statement in relation to the first statement. In logic, the converse of a conditional statement is formed by switching the hypothesis and conclusion. In this case, the first statement states that wearing blue implies being a senior, while the second statement states that being a senior implies wearing blue. Therefore, the second statement is the converse of the first statement.
9.
Which of the following statements means the same as:All medical doctors went to medical school.
Correct Answer
B. If you did not go to medical school, then you are not a medical doctor.
Explanation
The correct answer means that if someone did not attend medical school, they cannot be considered a medical doctor. This statement implies that the only way to become a medical doctor is by going to medical school. Therefore, if someone did not go to medical school, they cannot have the title of a medical doctor.
10.
What do we call the terms point, line and plane in Geometry?
Correct Answer
C. They are undefined terms.
Explanation
In geometry, point, line, and plane are considered as undefined terms. This means that they are not defined in terms of other geometric objects, but rather they are the basic building blocks from which all other geometric concepts are derived. These undefined terms serve as the foundation of geometry and are used to define other geometric objects and relationships.
11.
Three noncollinear points determine a plane. The statement above is considered a(n) ____________.
Correct Answer
D. Postulate
Explanation
The statement that three noncollinear points determine a plane is considered a postulate. A postulate is a basic assumption or statement that is accepted without proof. In this case, the postulate states a fundamental concept in geometry, that three points not lying on the same line uniquely determine a plane. This postulate serves as a starting point for further geometric reasoning and proofs.
12.
Points are collinear iff there is a line that contains all of them.The above statement is considered a(n) ____________
Correct Answer
A. Definition
Explanation
The given statement is considered a definition because it provides a clear and specific meaning for the term "collinear." It states that points are collinear if there exists a line that contains all of them. This definition helps us understand and identify collinear points in geometry.
13.
Which of the following are true about Triangle ABC if angle A = 40 degrees and Angle B = 100 degrees?I. Triangle ABC is obtuse.II. Triangle ABC is acute.III Triangle ABC is isosceles.
Correct Answer
E. I and III only
Explanation
The given information states that angle A is 40 degrees and angle B is 100 degrees. Based on this, we can determine that angle C must be 180 - (40 + 100) = 40 degrees.
I. Triangle ABC is obtuse: Since angle C is 40 degrees, which is less than 90 degrees, Triangle ABC is not obtuse. Therefore, this statement is false.
II. Triangle ABC is acute: Since angle C is 40 degrees, which is less than 90 degrees, Triangle ABC is acute. Therefore, this statement is true.
III. Triangle ABC is isosceles: Since angle A is 40 degrees and angle B is 100 degrees, these two angles are not equal. Therefore, Triangle ABC is not isosceles. Therefore, this statement is false.
Therefore, the correct statements are I (Triangle ABC is obtuse) and III (Triangle ABC is isosceles) only.
14.
The distance formula that allows you to find the length of a line segment depends on the formula:a^2 + b^2 = c^2, where a and b are the legs of a right triangle and c is the hypotenuse. This fact is an example of a(n)______________
Correct Answer
C. Theorem
Explanation
The given statement, a^2 + b^2 = c^2, is a well-known formula in geometry known as the Pythagorean theorem. It states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. The Pythagorean theorem is a proven mathematical statement that holds true for all right triangles, making it a theorem.
15.
The earth's circumference is approximately 25000 miles. City A and B are 2500 miles apart. At noon in City A, the sun is directly overhead. What is the angle the sun makes with standing objects in City B at the same time?
Correct Answer
36
36 degrees
Explanation
At noon, the sun is directly overhead in City A, which means it is at a 90-degree angle with standing objects in that city. Since City A and City B are 2500 miles apart and the earth's circumference is approximately 25000 miles, City B is 1/10th of the way around the earth from City A. Therefore, the angle the sun makes with standing objects in City B at the same time would also be 1/10th of 90 degrees, which is 36 degrees.
16.
How many circles are required to bisect a segment?
Correct Answer
2
Explanation
To bisect a segment, you need to divide it into two equal parts. This can be achieved by drawing a circle that intersects the segment at two points. The line connecting these two points on the segment will divide it into two equal parts. Therefore, only 2 circles are required to bisect a segment.
17.
How many circles are required to bisect an angle?
Correct Answer
3
Explanation
To bisect an angle, you need to draw two lines that divide the angle into two equal parts. One line can be drawn by using a straightedge, but to draw the second line, you need to use a compass to create an arc that intersects the angle's sides. This arc will intersect the angle's sides at two points, and by connecting these points to the angle's vertex, you will have bisected the angle. Therefore, you need to use at least one circle (compass) to bisect an angle, and a total of three circles (two arcs and one for the compass) are required.
18.
What is the best description in words of the Euler diagram below?
Correct Answer
C. It is a blip iff it is a blop.
Explanation
The correct answer is "It is a blip iff it is a blop." This statement accurately describes the relationship between blips and blops in the Euler diagram. It implies that any object in the diagram can only be classified as a blip if and only if it is also a blop, and vice versa. In other words, blips and blops are completely overlapping categories in the diagram.
19.
What conclusion can you make from the following statements?You had a stressful day today.If you walk fast, you will make it to school on time.If you wear sneakers, then your feet are comfortable.If you make it to school on time, you will not have a stressful day.If your feet are comfortable, then you can walk fast.
Correct Answer
B. You did not wear sneakers today.
Explanation
From the given statements, we can conclude that if you wear sneakers, then your feet are comfortable. However, the answer states that you did not wear sneakers today, which means that your feet were not comfortable.
20.
A. Martha is an only child.B. Martha has a brother.C. One of these statements is false.If all of the above statements are either True or False, which can you conclude?
Correct Answer
D. Statements B and C are true.
Explanation
The answer is "Statements B and C are true" because if all three statements were true, it would create a contradiction. If statement A were true, Martha would be an only child, but if statement B were also true, Martha would have a brother, which contradicts being an only child. Therefore, statement A cannot be true. This means either statement B or C must be false. Since we know that one of the statements is false, it confirms that statement C is true. Thus, the only remaining option is that statement B is also true.
21.
To prove that you cannot have two obtuse angles in a triangle, you start by assuming there exists a triangle in which there are two obtuse angles.What kind of proof are you beginning?
Correct Answer
B. Indirect