Download Definition of a Parallelogram:

Geometry Connections Chapter 7
Name:
7.2.1 All about Parallelograms
Period:
Definition of a Parallelogram:
7-44 A. Trace the triangle at right. Then rotate the shape 180˚ around the midpoint of one of the sides. Mark the
image with the angle markings,
What shape is the result. ______________________________________
What evidence to you have to back this up?
_________________________________________________________
B. If this truly is a parallelogram, what other information do you now know (be specific!)
about the sides? ______________________________________________________________________
and angles of the original parallelogram?___________________________________________________
C. Now we will start with a parallelogram and prove that this works for all parallelograms.
A
Given: ABCD is a Parallelogram
B
Prove:______________________ & ________________________
D
C
D. What about the diagonals of a parallelogram? What do they appear to do?
A
B
Given: ABCD is a parallelogram
Prove: Diagonals _____________
D
C
Geometry Connections Chapter 7
Name:
7.2.2 All about Rhombi ( or Rhombuses…. Whatever floats your boat)
Period:
Definition of a Rhombus:
7-54 What else appears to be true about the sides of a Rhombus?
Let’s prove it. What auxiliary lines do we need to draw?
What triangles would be useful to prove congruent?
Given: PQRS is a Rhombus.
Prove:
If this is true? What else do we then know about the diagonals of a Rhombus? Add this to your proof.
7-55 What to the diagonals do to each other and to the interior angles of a Rhombus? Remember 7.1.4
investigation?
Given: PQRS is a Rhombus
Prove:
7-56 Is there another way to prove that the opposite angles of
a parallelogram are congruent without using congruent triangles?
Given: TUVW is a parallelogram
Prove:
7-61 Jester started to prove that the triangles at right are congruent. He is only
told that point E is the midpoint of segments
and
. Complete his
flowchart below. Be sure that a reason is provided for every statement.
Geometry Connections Chapter 7
Name:
7.2.3 Rectangles and Kites
Period:
Definition of a Rectangle:
7-63
Given: ABCD is a Rectangle:
Prove: ABCD is a Parallelogram
What new facts do we now know about a rectangle?
Definition of a Kite:
B
7-47
Given: ABCD is a Kite
A
C
Prove: one set of opposite angles are congruent
& one diagonal bisects the interior angles.
D
Given: ABCD is a Kite (use PREVIOUS theorem and the definition)
B
Prove: the diagonals are perpendicular
& one diagonal bisects the other diagonal
A
C
D
Geometry Connections Chapter 7
Name:
7.2.4 Converse of Isosceles Triangle Theorem + Rectangle
Period:
71a
Isosceles Triangle Theorem:________________________________________________Converse:___________________________________________________________
Given:
Prove:
b.
Given: ABCD is a rectangle
A
B
D
C
Prove: the diagonals are ______________
c.
Thm: IIgram→opp sides are congruent
A
B
Converse:_____________________________________________
Given: both sets of opposite sides of a quadrilateral are congruent
Prove: ABCD is a parallelogram
D
C
A
d. REPEAT Given: ABCD is a rhombus
B
Prove: the diagonals bisect the interior angles
D
C
Geometry Connections Chapter 7
Name:
7.2.5 Squares and Isosceles Trapezoids
Period:
Take a proof from yesterday that you are confident is correct. Write it as a two column proof.
Statements:
Reasons:
Diagram
Definition of a Square:
Given: ABCD is a Square
A
B
D
C
Prove: ABCD is a Rectangle, Rhombus and Parallelogram
Definition of an Isosceles Trapezoid:
Given: ABCD is an Isosceles Trapezoid
Prove: the base angles are congruent
B
A
D
C
Given: ABCD is an Isosceles Trapezoid
A
B
Prove: the diagonals are congruent
D
C
Geometry Connections Chapter 7
Name:
7.2.6 Triangle mid segment theorem + more proofs
Period:
A
Given: One set of sides are II and congruent in a quadrilateral ABCD
B
Prove: ABCD is a IIgram
D
Given : Diags bisect each other
C
A
B
Prove: ABCD is a Parallelogram
D
C
7-88. TRIANGLE MIDSEGMENT THEOREM
As Sergio was drawing shapes on his paper, he drew a line segment that
connected the midpoints of two sides of a triangle. (This is called the midsegment
of a triangle.) “I wonder what we can find out about this midsegment,” he said to
his team. Examine his drawing at right.
1. EXPLORE: Examine the diagram of ΔABC , drawn to scale below. How do
you think DE is related to AB? How do their lengths seem to
be related?
2. CONJECTURE: Write a conjecture about the relationship
between segments DE and AB.
3. How are the triangles in the diagram related? How do you
know?
GIVEN: DE is the midsegment of triangle ABC
PROVE: ____________________
____________________
7-90
GIVEN: Two consecutive angles (A and D) are right angles in a quadrilateral
PROVE: ____________________
Geometry Connections Chapter 7
Name:
7.3.1 Coordinate Geometry + more proofs 
Period:
Try it again 
A
B
Given : Diags bisect each other
Prove: ABCD is a Parallelogram
D
C
Let’s look as some more converses….. are they always true or can be show a counterexample that would
disprove them?
Thm: Rhombus’s diags are perpendicular
Converse:
Draw a counterexample for the converse.
Thm. In a kite, one of the diags bisects the other diag.
Converse:
Draw a counterexample for the converse.
Thm. In a rectangle, the diags are congruent.
Converse:
Draw a counterexample for the converse.
7-98 Possible characteristics:
7-99 On graph paper, draw
and B(9, 2), and
15).
given A(0, 8)
given C(1, 3) and D(9,
1. Find the length of each segment.
2. Find the equation of
and the
equation of
. Write both
equations in y = mx + b form.
3. Is
4. Is
∥
⊥
?
? Justify your answers.
5. Use algebra to find the coordinates
of the point where
and
intersect.
7-100. AM I SPECIAL?
Shayla just drew quadrilateral SHAY, shown at right. The coordinates
of its vertices are:
S(0, 0) H(0, 5) A(4, 8) Y(7, 4)
1. Shayla thinks her quadrilateral is a trapezoid. Is she correct?
Justify your answer with evidence.
2. Does Shayla’s quadrilateral look like it is one of the other
kinds of special quadrilaterals you have studied? If so, which one and why?
3. Even if Shayla’s quadrilateral doesn’t have a special name, it may still have some special properties like
the ones you listed in problem 7-98. Use algebra and geometry tools to investigate Shayla’s
quadrilateral and see if it has any special properties. If you find any special properties, justify your
claim that this property is present.
7-101. THE MUST BE / COULD BE GAME
1.
2.
3.
4.
“My quadrilateral has four equal sides.”
“My quadrilateral has two pairs of opposite parallel sides.”
“My quadrilateral has two consecutive right angles.”
“My quadrilateral has two pairs of equal sides.”
Geometry Connections Chapter 7
Name:
7.3.2 Coordinate Geometry + more proofs 
Period: