### Given quadrilateral ABCD A(-4, 5) B(1, 1) C(-3, -4) D(

```Given quadrilateral QUAD
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the opposite sides QU and AD
congruent?
(Use the distance formula!)
QU 42 + 42 = d2
16 + 4 = d2
20 = d2
d = 20
NO, they
aren’t
congruent!
(different lengths)
82 + 42 = d2
64 + 16 = d2
80 = d2
d = 80
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the opposite sides AB and CD
congruent?
(Use the distance formula!)
AB
52 + 42 = d2
25 + 16 = d2
41 = d2
d = 41
CD
Yes, they are
congruent!
(same lengths)
52 + 42 = d2
25 + 16 = d2
41 = d2
d = 41
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Do the diagonals bisect each other?
(Use the midpoint formula!)
NO, they
don’t bisect
each other!
(not same midpoint)
QA
−3+ 4
2
=
1
2
1+2 3
=
2
2
(.5, 1.5)
UD
1+ −4
2
=
−3
2
3 + −2 1
=
2
2
(-1.5, .5)
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the opposite sides AD and BC
parallel?
Yes, they are
(Use the slope formula!)
0 −5
−8 −−4
=
−5
−4
parallel!
(same slopes)
5
=
4 −4−1
BC
−3 −1
=
−5
−4
=
5
4
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the diagonals perpendicular?
(Use the slope formula!)
AC
−4 −5
−3 −−4
=
Yes, they are
perpendicular!
(b/c the slopes are opp recips)
−9
0 −1
BD
1
−8 −1
=
−1
−9
=
1
9
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the opposite sides AB and CD
parallel?
Yes, they are
(Use the slope formula!)
AB
1 −5
1 −−4
=
−4
CD
5
parallel!
(same slopes)
0 −−4
−8 −−3
=
4
−5
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the diagonals perpendicular?
(Use the slope formula!)
2 −1
QA
4 −−3
=
1
7
NO, they aren’t
perpendicular!
(b/c the slopes aren’t opp recips)
−2 −3
UD
−4 −1
=
−5
−5
=1
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the opposite sides UA and QD
congruent?
(Use the distance formula!)
UA
32 + 12 = d2
9 + 1 = d2
10 = d2
d = 10
QD 12 + 32 = d2
1 + 9 = d2
10 = d2
d = 10
Yes, they are
congruent!
(same lengths)
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the opposite sides QU and AD
parallel?
Yes, they are
(Use the slope formula!)
3−1
QU
1−−3
2
4
= =
1
2
parallel!
(same slopes)
−2−2
−4 −4
=
−4
−8
=
1
2
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the opposite sides BC and AD
congruent?
(Use the distance formula!)
BC
42 + 52 = d2
16 + 25 = d2
41 = d2
d = 41
Yes, they are
congruent!
(same lengths)
42 + 52 = d2
16 + 25 = d2
41 = d2
d = 41
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the opposite sides UA and QD
parallel?
NO, they aren’t
(Use the slope formula!)
2−3
UA
4−1
=
parallel!
(different slopes)
−1
−2 −1
QD
3
−4 −−3
=
−3
−1
=3
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the diagonals congruent?
(Use the distance formula!)
AC
12 + 92 = d2
1 + 81 = d2
82 = d2
d = 82
BD
12 + 92 = d2
1 + 81 = d2
82 = d2
d = 82
Yes, they are
congruent!
(same lengths)
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the consecutive sides AB and BC
perpendicular?
Yes, they are
perpendicular!
(Use the slope formula!)
AB
1 −5
1 −−4
=
−4
5
(slopes opp reciprocals)
BC
−4−1
−3 −1
=
−5
−4
=
5
4
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the consecutive sides QU and UA
perpendicular?
NO, they aren’t
(Use the slope formula!)
3−1
QU
1−−3
2
4
= =
1
2 UA
perpendicular!
(slopes not opp reciprocals)
2−3
4−1
=
−1
3
Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Are the diagonals congruent?
(Use the distance formula!)
QA 72 + 12 = d2
49 + 1 = d2
50 = d2
d = 50
Yes, they are
congruent!
(same lengths)
UD 52 + 52 = d2
25 + 25 = d2
50 = d2
d = 50
A(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Do the diagonals bisect each other?
Yes, they bisect
each other!
(Use the midpoint formula!)
(same midpoint)
AC
−4+ −3
2
=
−7
2
5 + −4 1
=
2
2
(-3.5, .5)
BD
1+ −8
2
=
−7
2
1+0 1
=
2
2
(-3.5, .5)
```