Questions from McDougal Littell, Geometry, 2007.
Squares, Rectangles, and
Rhombi!
Squares, Rectangles, and Rhombi
Statements
and Converses
One Big Figure
Rectangles and Grab Bag 
Rhombi
Review!
200
200
200
200
200
400
400
400
400
400
600
600
600
600
600
800
800
800
800
800
1000
1000
1000
1000
1000
Bonus Question: 5000 pts
Topic 1: 200
• Question:
• Is the statement true? What about its
converse?
– If a quadrilateral is a rectangle, then it is a
parallelogram.
• Answer
– A rectangle is always a parallelogram, but a
parallelogram isn’t necessarily a rectangle.
Topic 1: 400
• Question:
• Is the statement true? What about its
converse?
– If a quadrilateral is a parallelogram, then it is a
rhombus.
• Answer
– A parallelogram isn’t necessarily a rhombus, but a
rhombus is always a parallelogram.
Topic 1: 600
• Question:
• Is the statement true? What about its
converse?
– If a quadrilateral is a square, then it is a rhombus.
• Answer
– A square is also a rhombus, but a rhombus isn’t
necessarily a square.
Topic 1: 800
• Question:
• Is the statement true? What about its
converse?
– If a quadrilateral is a rectangle, then it is a
rhombus.
• Answer
– A rectangle isn’t necessarily a rhombus, and a
rhombus isn’t necessarily a rectangle.
Topic 1: 1000
• Question:
– If a statement and its converse are true, how can
you make a new statement which incorporates
both?
• Answer
– If a statement and its converse are both true, then
it is a biconditional statement. You can reword it
into an “if and only if” statement to show that
both “sides” hold.
• Question:
– BGED is a rectangle and
ABCD is a rhombus, find
the measure of ∠GDB
• Answer
– m∠GDB = 27˚
Topic 2: 200
• Question:
– BGED is a rectangle and
ABCD is a rhombus, find
the measure of ∠ABC
• Answer
– m∠ABC = 54˚
Topic 2: 400
• Question:
– BGED is a rectangle and
ABCD is a rhombus, find
the measure of ∠DAB
• Answer
– m∠DAB = 126˚
Topic 2: 600
• Question:
– BGED is a rectangle and
ABCD is a rhombus, find
the measure of ∠GCE
• Answer
– m∠GCE = 126˚
Topic 2: 800
• Question:
– BGED is a rectangle and
ABCD is a rhombus.
• List all of the triangles
which are congruent in the
figure.
• Answer
– ΔABH, ΔADH, ΔCHD,
ΔCBH, and the bottom
triangles with
hypotenuses of CG and
CE are all congruent.
Topic 2: 1000
Topic 3: 200
• Question:
– Find m∠URV
• Answer
– m∠URV = 71˚
Topic 3: 400
• Question:
– Find the length of RT.
• Answer
– Length RT = 28.65
Topic 3: 600
• Question:
– Find m∠RVT
• Answer
– m∠RVT = 38˚
Topic 3: 800
• Question:
– Find m∠XWO
• Answer
– m∠XWO = 34˚
Topic 3: 1000
• Question:
– Find the length of
WZ.
• Answer
– Length WZ = 18.45
Topic 4: 200
• Question:
– Classify the quadrilateral and then solve for ‘x’
and ‘y’.
• Answer
– The quadrilaterals is a square, while x = 4 and y
= 9.
Topic 4: 400
• Question:
– Classify the quadrilateral, and then solve for ‘x’
and ‘y’.
• Answer
– The figure is a rhombus, while x = 5 and y = 11.
Topic 4: 600
• Question:
– Draw the figure, and then solve
• Answer
– Length XY = 11
Topic 4: 800
• Question:
– Draw the figure and then solve.
• Answer
– m∠Y = 60˚
Topic 4: 1000
• Question:
– Draw the figure and then
solve.
• Answer
– Length WY = 10
Topic 5: 200
• Question:
• Answer
– The slope of MN is (3/11) and PQ is (3/11), while
the slope of MQ is (-5/4) and NP is (-5/4), so there
are two pairs of parallel sides, so the MNPQ is a
parallelogram.
Topic 5: 400
• Question:
• Answer
– The distances of MN and PQ are 11.4, while the
distances of NP and MQ are 6.4, so there are two
pairs of congruent sides, meaning MNPQ must be
a parallelogram.
• Question:
Topic 5: 600
• Answer
– Because the diagonals are bisected, set 12x + 1 = 49
and 8y + 4 = 36. This gives x = 4 and y = 4.
• Question:
Topic 5: 800
• Answer
– Let x = the first angle, and y = the adjacent angle.
Recognize that x = 3y – 12 and y = 180 – x. Plugging
in, one gets x = 132, so y = 48. One of the other
interior angles is also 132, and another is 48.
• Question:
Topic 5: 1000
• Answer
– The polygon has 5 sides; the interior angles sum to
540, and as always, the exterior angles sum to 360.
• Question:
– Can claim that JANE is a more
specific type of quadrilateral?
Explain.
Bonus Question:
5000 pts.
• Answer
– Because JANE is a parallelogram,
we already know its opposite sides
are congruent. To show the angles
of JANE are all 90, note that
because JXPE is a parallelogram
and XP is perpendicular to EN, PX is
also perpendicular to JA. This
implies that m∠PEA, m∠XJE,
m∠PNA, and m∠XAN are all 90˚
because of alternate interior
angles. Thus, JANE is a rectangle.
Daily Double
Write down how much money you are willing to risk.
If you get the question right, you win that money;
if you get it wrong you lose it!
Daily Double
Write down how much money you are willing to risk.
If you get the question right, you win that money;
if you get it wrong you lose it!