Ines often has a few drinks when she goes to a party. She knows that it is against the law but since she does not do it very often, she doesn’t think it is a big deal. What BEST describes Ines’s behavior?
Proactive
High Risk
Addictive
Compulsory
High Risk
Image shows line WS and line KV as parallel. Line RT intersects line WS and line KV forming right angles.
Line WS is parallel to line KV. Line RT is perpendicular to line KV. Explain the relationship of line RT to line WS. Provide at least one reason to support your answer.
Line RT is not necessarily parallel or perpendicular to line WS. The given information only tells us that line RT is perpendicular to line KV. The relationship between line RT and line WS cannot be determined without additional information or measurements.
Logan has 64 inches of trim to make a picture frame. Since he wants to use all of the trim, he decides to make a square frame measuring 8 inches on each side. Did Logan correctly determine the correct frame size? Explain.
A.
Yes; since
8
×
8
=
64
, Logan will use all of the trim.
B.
Yes;
8
+
8
=
16
. Since the four sides of the square are equal and
4
×
16
=
64
, Logan will use all of the trim.
C.
Yes; since
64
÷
4
=
16
, Logan will use all of the trim.
D.
No;
8
×
8
=
64
is the area of the rectangle. Logan should find a square with a perimeter of 64, not an area equal to 64.
B. Yes; 8 + 8 = 16. Since the four sides of the square are equal and 4 x 16 = 64, Logan will use all of the trim.
Logan correctly determined the frame size. The perimeter of the square frame is 4 x 8 = 32 inches, which means that each side of the square is 8 inches, and the total length of trim required is 4 x 8 = 32 inches. Since Logan has 64 inches of trim, he can make two such frames.
How many lines of symmetry can a rhombus have?
Select numbers from the drop-drop menus to complete your answer.
Rhombuses have
Choose...
lines of symmetry. Rhombuses that are also squares have
Choose...
lines of symmetry.
Rhombuses have 2 lines of symmetry. Rhombuses that are also squares have 4 lines of symmetry.
Image shows left half of arrow pointing upward.
Which choice completes the drawing so it is line symmetric?
A.
Image shows top half of horizontal arrow pointing to the right.
B.
Image shows right side of arrow pointing downward.
C.
Image shows left half of arrow pointing upward.
D.
Image shows right half of arrow pointing upward.
D. Image shows right half of arrow pointing upward.
If we draw the right half of the arrow pointing upward, it will complete the drawing so it is line symmetric. This is because the left and right halves of the arrow will be mirror images of each other across the axis of symmetry.
Robert says that he can draw an obtuse equilateral triangle. Jonas says that is not possible. Who is correct and why?
A.
Robert is correct as long as the other two angles are acute and all of the sides are the same length.
B.
Jonas is correct because an equilateral triangle has 3 acute angles and all sides the same length.
C.
Robert is correct because all equilateral triangles have 1 obtuse angle and all sides the same length.
D.
Jonas is correct because equilateral triangles have one right angle and two sides the same
B. Jonas is correct because an equilateral triangle has 3 acute angles and all sides the same length.
An equilateral triangle, by definition, has three equal sides and three equal angles. Since all angles in an equilateral triangle must be equal, it is not possible for one of them to be obtuse, which is an angle greater than 90 degrees. Therefore, Jonas is correct - it is not possible to draw an obtuse equilateral triangle.
Which statement is true about trapezoids?
A.
A trapezoid is a quadrilateral with only one pair of parallel sides.
B.
A trapezoid is a parallelogram with two pairs of parallel sides.
C.
A trapezoid is a quadrilateral with two pairs of parallel sides.
D.
A trapezoid is a parallelogram with only one pair of parallel sides.
C. A trapezoid is a quadrilateral with two pairs of parallel sides.
By definition, a trapezoid is a quadrilateral with at least one pair of parallel sides. Therefore, it can have more than one pair of parallel sides, but it is not guaranteed. Options A and D are incorrect because they describe the opposite extremes of the possible number of parallel sides. Option B is incorrect because it describes an entirely different type of quadrilateral - a parallelogram - which has two pairs of parallel sides, but different angle measures than a trapezoid.
Part A.
Jill said that the polygons shown have the same number of angles as they have sides. Select the correct choice to critique Jill's reasoning.
A.
Count the number of sides and angles of a polygon that has more sides than angles.
B.
Count the number of sides and angles each polygon has.
C.
Count the number of sides and angles the largest polygon has.
D.
Count the sides of the polygons to make sure they each have four.
Part B.
Explain whether Jill's reasoning makes sense.
Jill's reasoning
Choose...
make sense. There
Choose...
the same number of angles as there are sides of a polygon.
Part A:
B. Count the number of sides and angles each polygon has.
Part B:
Jill's reasoning does not make sense. Jill's statement is only true for regular polygons, where all sides and angles are congruent. However, the polygons shown in the figure are not all regular. In general, the number of sides in a polygon does not have to be equal to the number of angles. In fact, it is possible to construct polygons with any number of sides and angles. Therefore, Jill's statement needs to be corrected to reflect the fact that it only applies to regular polygons, not all polygons.
Which describes an acute isosceles triangle?
A.
two sides of equal length, all angles are less than 90 degrees
B.
three sides of equal length, one 90 degree angle
C.
no sides the same length, two angles less than 90 degrees
D.
no sides the same length, on angle greater than 90 degrees
A. two sides of equal length, all angles are less than 90 degrees
An acute isosceles triangle is a triangle with two sides of equal length (making it isosceles) and all angles less than 90 degrees (making it acute). Option B describes a right isosceles triangle, while options C and D describe different types of obtuse triangles.
Image shows an isosceles triangle.
The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides?
Explain how you know. Provide at least one reason for your answer.
Let's call each of the equal sides of the isosceles triangle "x".
We know that the perimeter of the triangle is 22 cm.
Perimeter = sum of all sides of the triangle
So we can set up an equation:
x + x + 6 = 22
Simplifying, we get:
2x + 6 = 22
Subtracting 6 from both sides:
2x = 16
Dividing by 2:
x = 8
Therefore, each of the equal sides of the triangle must be 8 cm long.
Explanation:
We know that the two equal sides of the isosceles triangle must have the same length. Let's call that length "x". We also know that one of the sides is 6 cm long. When we add up all three sides of the triangle, we get the perimeter of 22 cm. We can use these three pieces of information to set up an equation to solve for "x". Once we find the value of "x", we can confirm that it is the correct value by plugging it back into the equation and verifying that the sum of the three sides is indeed 22 cm. Since the triangle is isosceles, we know that the other two sides must have the same length, so each side must be 8 cm long.
Part A
Jan says that a rhombus is a parallelogram and that every parallelogram is also a rhombus. Is Jan correct?
Part B
Explain why or why not.
Part A:
No, Jan is not correct.
Part B:
A rhombus is a type of parallelogram, but not all parallelograms are rhombuses. A rhombus is a parallelogram with four congruent sides. However, a parallelogram can have two pairs of congruent sides that are not all equal in length. Therefore, all rhombuses are parallelograms, but not all parallelograms are rhombuses.
Therefore, Jan's statement is not entirely accurate.
Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
Image shows a snowflake with six points.
A.
no
B.
yes; 3 lines of symmetry
C.
yes; 6 lines of symmetry
D.
yes; 12 lines of symmetry
C. Yes; 6 lines of symmetry.
The figure is line symmetric because it can be divided into six congruent parts that are mirror images of each other. Therefore, it has six lines of symmetry - one for each point of the star shape.
ow many lines of symmetry does an equilateral triangle have?
An equilateral triangle is shown.
A.
0
B.
1
C.
2
D.
3
C. 2.
An equilateral triangle has two lines of symmetry. One line of symmetry is the perpendicular bisector of the base, which divides the triangle into two congruent right triangles. The other line of symmetry is a line that goes from one vertex to the midpoint of the opposite side, dividing the triangle into two congruent isosceles triangles.
Kathleen says that all quadrilaterals have right angles. Grace says that quadrilaterals do not have to have right angles. Explain who is correct.
A.
Kathleen is correct because rectangles have four right angles.
B.
Grace is correct because quadrilaterals have no right angles.
C.
Kathleen is correct because quadrilaterals have four equal angles.
D.
Grace is correct because a rhombus may not have right angles.
B. Grace is correct because quadrilaterals do not have to have right angles.
While rectangles have four right angles, not all quadrilaterals are rectangles. Kathleen's statement is only true for rectangles, not all quadrilaterals. In fact, there are many quadrilaterals that do not have any right angles, such as parallelograms, trapezoids, and kites. Therefore, Grace is correct - quadrilaterals do not have to have right angles.
Options C and D provide irrelevant or incorrect information, respectively, and do not address the question of whether all quadrilaterals have right angles.