Download 2 - Proving Parallelograms

Geometry Notes Q – Proving quadrilaterals are parallelograms
Proving a quadrilateral is a parallelogram: A quadrilateral is a parallelogram if
1.
or 2.
or 3.
or 4.
or 5.
Ex: Determine if each of the following is a parallelogram and give a reason.
A
B
x+1
x2  13
D
3x  3
1
(4x + 2)
2x  4
C
Theorem: The diagonals of a parallelogram
A
B
Given: Parallelogram ABCD, diagonals
AC and BD intersect at E.
Prove: AC and BD
E
D
C
E
Ex: Parallelogram EASY has diagonals intersecting at R. Find
the lengths of the diagonals.
A
x
2y – 8
Y
x+4
R
y–2
S
Name:______________________
Geometry
Date:___________
Parallelogram HW
1. In parallelogram GRAM, mG = x2 and mR = 12x + 20. Find the measures of all four angles of GRAM.
2.
In each diagram, assume the quadrilateral that looks like a parallelogram is one and that points that appear
collinear are collinear. Copy each diagram onto your paper and find the value of the variable(s).
a.
x
100
35
b.
c.
70
x
110
y
x
3. In parallelogram ABCD, diagonal AC is congruent to side AB and mBAC = 30. Find the value of
a. mB
b. mBCD
4. Given: Parallelogram PQRS, QWVS , PV  QS , WR  QS .
Prove: QPV  SRW
5. Two vertices of parallelogram PGRM are P(3, 2) and G(4, 6). The diagonals intersect at A(7, 5). Find the
coordinates of R and M.
6. In parallelogram ABCD at right, E is a point on BD such that
AE  BD , mDAE = 50, and mBDC = 30. Find mC.
A
B
E
D
7.
C
In the figures below, the givens are marked on the diagram (arcs indicate congruent angles, slashes indicate
congruent segments, and arrows indicate parallel segments). Tell whether the figure must be a
parallelogram and if so, give a specific reason.
a.
b.
c.
d.
e.
f.
g.
h.