NAME
_
DATE
_
SCORE
_
Practice 54
Coordinate Geometry Proofs
Supply the missing coordinates without introducing any new letters.
1. Rectangle
2. Parallelogram
y
y
O(?, ?)
(0, a) 1 - - - - - - - , P(?, ?)
(d, e)
o
(b,O)
o
x
P(.----)
x
Q(----)
4. Equilateral Triangle
. 3. Isosceles Trapezoid
y
y
(0/)
R(?, ?)
(g, h)
o
S(?,?)
x
R(
)
0
S(.
x
(j, 0)
), T(
)
5. Use coordinate geometry to prove that the diagonals of a square
are congruent. First draw a figure and choose convenient axes
and coordinates.
6. Isosceles right triangle OBe with median OM is shown in the
diagram. Find the coordinates of M and use coordinate geometry
to prove that OM ..L Be.
y
C(0,2a)
o
M(
164
x
B(2a, 0)
)
RESOURCE BOOK for GEOMETRY
Copyright © by Houghton Mifflin Company. All rights reserved.
NAME
_
DATE
SCORE
_
Coordinate Geometry Proofs
Supply the missing coordinates without introducing any new letters.
1. Rectangle
2. 30°- 60°- 90° triangle
y
3. Equilateral triangle
y
y
O(O,d)
0(0,0)
x
o
o
B(h.O)
C=
CO, 7) 0
E=
_
_
H(h.O)
G=
_
1=
Supply the missing statements and reasons to complete the proof
that a diagonal of a parallelogram divides the parallelogram into two
congruent triangles.
y
O(d, c)
C(b+d, c)
4. Given: LJOBCD
.r
Prove: 60BC == 6CDO
o
B (h, 0)
Proof:
Statements
Reasons
1.
1. OBCD is a parallelogram.
2. OB
OD
= ViI;
CD
= Yd + c
2
2
;
= ViI;
BC
2.'
= Vd +
2
c
_
2
3. OB = CD; OD = BC
3.
.4. ~--~-------------
4. Reflexive Property
5. OB == CD; OD == BC
5.
6.
6.
5. Use coordinate geometry to prove that the midpoint of the
hypotenuse of a right triangle is equidistant from the vertices.
---------­
y
Given: M is the midpoint of the hypotenuse of right 60AB.
Prove: MO = MA = MB
Proof:
x
o
A (20. 0)
i
1
I
I
1
1
1
·1
PRACTICE MASTERS for GEOMETRY
Copyright © by Houghton Mifflin Company. All rights reserved.
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