Download (2) (1) The answer is correct, so the grade should be 10 points (2

(2) (1) The answer is correct, so the grade should be 10 points
(2) The answer is correct, so the grade should be 10 points
(3) The student did make a figure worth 10 points, but they made a square
not a trapezoid. I would give them a grade of 5 points
(3) (a)
(b)
(c)
(d)
The
The
The
The
figure
figure
figure
figure
is closed and has 4 sides so it is a quadrilateral
is closed and has 4 sides so it is a quadrilateral
has 5 sides not 4 so it’s a pentagon, not a quadrilateral
has a curve instead of a side, so it is not a quadrilateral
(5) The numbers ordered from least to greatest are −5/2, −2, 0, 5/4, 3/2. Your
paper should also have a number line with these numbers clearly marked.
(a) The figure has 2 pairs of parallel sides, so it is a parallelogram
(b) The figure has only one pair of parallel sides, so it is a trapezoid. Because
the non-parallel sides are congruent, it is an isoceles trapezoid.
(c) The figure is convex and has exactly 2 pairs of adjacent congruent sides,
so it is a kite.
(d) he figure has only one pair of parallel sides, so it is a trapezoid.
(13) (a) Since opposite angles of parallelograms are congruent, x = 47.
(b) Since opposite angles of parallelograms are congruent, we know that the
four angles measure 110, 110, x, and x. Since the sum of the angles is
360, x + x + 110 + 110 = 360. Hence 2x + 220 = 360. So 2x = 140, and
hence x = 70.
(20) (a) This is sometimes true. A square is a rectangle with 4 congruent sides, so
a square is both a rectangle and a rhombus. However, there are rectangles
that don’t have 4 congruent sides, and these are not rhombuses.
(b) A rhombus is never a kite. A kite has exactly 2 pairs of adjacent sides
that are congruent, but in a rhombus all sides are congruent, so there are
more than just 2 pairs of adjacent sides that are congruent
(c) This is always true. Because the trapezoid has one pair of parallel sides
it is always convex.
(d) This is never true. If the parallel side of an isoceles trapezoid where
congruent, then the other 2 sides would have to be parallel and the figure
would be a parallelogram, not a trapezoid.
(22) (a) 116 + 64 = 180 so the adjacent angles are supplementary.
(b) This property does hold for all parallelograms. Suppose that 2 adjacent
angles of a parallelogram have measure x degrees and y degrees. Then
the other 2 angles have measure x degrees and y degrees because they
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are opposite the first 2 angles and opposite angles of a parallelogram are
congruent. Since the sum of the angles of a quadrilateral is 360, we know
that x + x + y + y = 360. So 2x + 2y = 360. Hence 2(x + y) = 360.
Dividing both sides by 2 gives us x+y = 180. Since the sum of 2 adjacent
angles is 180, the angles are supplementary.
(c) One activity would be to have students draw and cut out a parallelogram,
and label 2 adjacent angles a and b. Then they would trace and cut out a
copy of the parallelogram. Next I would have them place angles a and b
together and see that a straight line is made. This shows that the angles
are supplementary.
(26) (a)
(b) The triangle has a right angle so it is a right triangle
(c) The quadrilateral has 4 right angles, so it is a rectangle. It also has 4
congruent sides, so it is a square.
(36) The student thought that the measure of the missing angle was equal to the
measure of the opposite angle, but this is only true if the shape is a parallelogram. The student should have added the measures of the 4 angles, including
the missing angle together and set it equal to 360 since the sum of the measures of the angles of a quadrilateral is 360. Then they can solve for x. So
103 + 72 + 125 + x = 360. Hence 300 + x = 360. So x = 60. I would encourage the student to review the section on the sum of the angle measures of a
quadrilateral.