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Given quadrilateral QUAD Q(-3, 1) U(1, 3) A(4, 2) D(-4, -2). NO, they aren’t congruent! (different lengths). (Use the distance formula!). Are the opposite sides QU and AD congruent?. QU4 2 + 4 2 = d 2 16 + 4 = d 2 20 = d 2 d = . AD8 2 + 4 2 = d 2 64 + 16 = d 2 - PowerPoint PPT Presentation
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Are the opposite sides QU and AD congruent?
(Use the distance formula!)
QU 42 + 42 = d2
16 + 4 = d2
20 = d2
d =
AD 82 + 42 = d2
64 + 16 = d2
80 = d2
d =
NO, they aren’t congruent!(different lengths)
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Given quadrilateral ABCDA(-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 =
CD 52 + 42 = d2
25 + 16 = d2
41 = d2
d =
Yes, they are congruent!(same lengths)
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
(Use the midpoint formula!)NO, they don’t bisect each other!(not same midpoint)
Do the diagonals bisect each other?
QA
(.5, 1.5)
UD
(-1.5, .5)
Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
(Use the slope formula!)
AD
BC
Yes, they are parallel!(same slopes)
Are the opposite sides AD and BC parallel?
Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
Are the diagonals perpendicular?
(Use the slope formula!)
AC BD
Yes, they are perpendicular!(b/c the slopes are opp recips)
Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
(Use the slope formula!)
AB CD
Yes, they are parallel!(same slopes)
Are the opposite sides AB and CD parallel?
Are the diagonals perpendicular?
(Use the slope formula!)
QA UD
NO, they aren’t perpendicular!(b/c the slopes aren’t opp recips)
Given quadrilateral QUADQ(-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 =
QD 12 + 32 = d2
1 + 9 = d2
10 = d2
d =
Yes, they are congruent!(same lengths)
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
(Use the slope formula!)
QU
AD
Yes, they are parallel!(same slopes)
Are the opposite sides QU and AD parallel?
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Given quadrilateral ABCDA(-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 =
AD 42 + 52 = d2
16 + 25 = d2
41 = d2
d =
Yes, they are congruent!(same lengths)
(Use the slope formula!)
UA QD
NO, they aren’t parallel!(different slopes)
Are the opposite sides UA and QD parallel?
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Given quadrilateral ABCDA(-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 =
BD 12 + 92 = d2
1 + 81 = d2
82 = d2
d =
Yes, they are congruent!(same lengths)
Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
(Use the slope formula!)
BC
Yes, they are perpendicular!(slopes opp reciprocals)
Are the consecutive sides AB and BC perpendicular?
AB
(Use the slope formula!)
NO, they aren’t perpendicular!(slopes not opp reciprocals)
Are the consecutive sides QU and UA perpendicular?
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
QU UA
Are the diagonals congruent?
(Use the distance formula!)
QA 72 + 12 = d2
49 + 1 = d2
50 = d2
d =
UD 52 + 52 = d2
25 + 25 = d2
50 = d2
d =
Yes, they are congruent!(same lengths)
Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2)
Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0)
(Use the midpoint formula!) Yes, they bisect each other!(same midpoint)
Do the diagonals bisect each other?
AC
(-3.5, .5)
BD
(-3.5, .5)
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