Math Exam 2
standard deviation has the following characteristics.
1.About 68% of the data lie within one standard deviation of the mean. 2. About 95% of the data lie within two standard deviations of the mean. 3. About 99.8% of the data lie within three standard deviations of the mean.
90-a
90-a
Regular hexagons have been used to tile floors. Can a floor be tiled using only regular pentagons? Why or why not?
A floor cannot be tiled using only regular pentagons. For a regular hexagon, the measure of each vertex angle is 120degrees, which means that three regular hexagons fit to form 360degrees, and the plane can be filled. For a regular pentagon, the measure of each vertex angle is 108degrees, so regular pentagons cannot be placed together to fill the plane because the measure of the plane, 360degrees, is not divisible by the measure of each vertex angle.
Identify a physical object to represent: Skew lines
A horizontal and vertical edge of a cube that do not share a vertex
Two properties that hold true for all rectangles but not for all rhombuses
All angles must be right angles & All diagonals are the same length.
Two properties that hold true for all squares but not for all isosceles trapezoids
All angles must be right angles & All sides are the same length.
. What kind of quadrilateral is ABCD? Justify your answer.
Because the sum of the interior angles is 360degrees, angleA and angleD are supplementary. Also, angleD and angleC are supplementary. If we extend the side AD to form an alternate interior angle to angleC, we see that these angles are congruent and thus, BC is parallel to AD. Similarly, AB is parallel to DC. Thus, ABCD is a parallelogram.
Write a note to another student explaining the difference between a right prism and an oblique prism.
If the lateral faces are rectangles, then the prism is a right prism,and if some are non-rectangular parallelograms, then the prism is an oblique prism.
How does this sixth grade geometry common core type question meet the goals behind the common core standards?
It assesses students' understanding of the properties of cubes, as well as their ability to find multiple ways to create a cube.
If one angle of a triangle is obtuse, can another also be obtuse? Why or why not?
No, because the sum of two obtuse angles is more than 180degrees
Can a triangle have two right angles? Why or why not?
No, because the sum of two right angles is 180degrees, thus the sum of the three angles of the triangle would be more than 180degrees.
If a triangle has one acute angle, is the triangle necessarily acute? Why or why not?
No, because you can have a right or an obtuse triangle with one acute angle.
How are pairs of parallel lines and skew lines different?
Parallel lines and skew lines are different in that parallel lines are coplanar and skew lines are not coplanar.
How are pairs of parallel lines and skew lines similar?
Parallel lines and skew lines are similar in that they do not intersect.
If planes alpha and beta are distinct planes having points A, B, and C in common, what conclusion can be made about points A, B, and C?
Points A, B, and C are collinear because if two distinct planes intersect, the intersection is a line and the common points must all lie on that line.
How does this fifth grade common core type geometry question challenge a student's understanding of shapes?
Students must know shapes and their properties, as well as what subcategories the shapes belong to based on their properties.
T OR F : Two intersecting lines are coplanar.
TRUE
T OR F: A line segment contains an infinite number of points.
TRUE
T OR F: Three noncollinear points are always coplanar.
TRUE
Identify a physical object to represent: Parallel planes
The covers of a book
Identify a physical object to represent: A right angle
The edge of a table and one leg of that table meeting that edge
Identify a physical object to represent: Parallel lines
The opposite edges of the side of a table
Jane heard a student say that all squares are rectangles but not all rectangles are squares. She said this did not sound correct. How do you respond?
The statement is correct. A rectangle is a parallelogram with four right angles. A square has four right angles and four equal sides, so a square is a rectangle. A rectangle does not have to have four equal sides.
T OR F: The union of two rays is always a line.
The statement is false because the union of two rays can be a single ray.
T OR F: Two planes can intersect in exactly one point.
The statement is false because they can intersect in a line, the empty set, or a plane.
A student claims that if any two planes that do not intersect are parallel, then any two lines that do not intersect should also be parallel. How do you respond?
The student is incorrect. Two distinct lines are parallel if they do not intersect and are in a single plane. Lines that do not intersect and are not in a single plane are called skew lines.
Two properties that hold true for all parallelograms but not for all squares
This is impossible. All squares are parallelograms.
How many possible pairs of bases does a rectangular prism have?
Three. Each pair of parallel faces could be considered bases.
complementary angles
Two angles whose sum is 90 degrees
Are all equilateral triangles isosceles? Explain.
Yes, because according to the definition, isosceles triangles have at least two congruent sides. Equilateral triangles have three congruent sides. Therefore, they have at least two congruent sides and are isosceles.
If one angle of a triangle is acute, can the other two angles also be acute? Why or why not?
Yes, because three angles that are less than 90degrees can sum to 180degrees
closed curve
a curve that begins and ends at the same point
simple curve
a curve that does not intersect itself
parallel lines
coplanar
skew lines
non-coplanar lines that do not intersect
he measure of an exterior angle of any triangle equals
the sum of the measures of the two remote interior angles.
SD
thing 1-thing2 /SD
summplementary angles
two angles that add up to 180 degrees
Can a regular polygon be concave?
No, a concave polygon has at least one angle greater than 180 degrees and some angles less than 180 degrees. Therefore, the figure cannot have all the same angles and cannot be a regular polygon.