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Are the opposite sides QU and AD congruent?

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?. QU 4 2 + 4 2 = d 2 16 + 4 = d 2 20 = d 2 d = . AD 8 2 + 4 2 = d 2 64 + 16 = d 2

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Are the opposite sides QU and AD congruent?

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  1. Given quadrilateral QUADQ(-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? QU 42 + 42 = d2 16 + 4 = d2 20 = d2 d = AD 82 + 42 = d2 64 + 16 = d2 80 = d2 d =

  2. Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are congruent! (same lengths) (Use the distance formula!) Are the opposite sides AB and CD congruent? AB 52 + 42 = d2 25 + 16 = d2 41 = d2 d = CD 52 + 42 = d2 25 + 16 = d2 41 = d2 d =

  3. Do the diagonals bisect each other? NO, they don’t bisect each other! (not same midpoint) Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) (Use the midpoint formula!) UD (-1.5, .5) QA (.5, 1.5)

  4. Are the opposite sides AD and BC parallel? Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are parallel! (same slopes) (Use the slope formula!) AD BC

  5. Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are perpendicular! (b/c the slopes are opprecips) (Use the slope formula!) Are the diagonals perpendicular? AC BD

  6. Are the opposite sides AB and CD parallel? Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are parallel! (same slopes) (Use the slope formula!) AB CD

  7. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) NO, they aren’t perpendicular! (b/c the slopes aren’t opprecips) (Use the slope formula!) Are the diagonals perpendicular? QA UD

  8. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) Yes, they are congruent! (same lengths) (Use the distance formula!) Are the opposite sides UA and QD congruent? UA 32 + 12 = d2 9 + 1 = d2 10 = d2 d = QD 12 + 32 = d2 1 + 9 = d2 10 = d2 d =

  9. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) Are the opposite sides QU and AD parallel? Yes, they are parallel! (same slopes) (Use the slope formula!) QU AD

  10. Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are congruent! (same lengths) (Use the distance formula!) Are the opposite sides BC and AD congruent? BC 42 + 52 = d2 16 + 25 = d2 41 = d2 d = AD 42 + 52 = d2 16 + 25 = d2 41 = d2 d =

  11. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) Are the opposite sides UA and QD parallel? NO, they aren’t parallel! (different slopes) (Use the slope formula!) UA QD

  12. Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are congruent! (same lengths) (Use the distance formula!) Are the diagonals congruent? AC 12 + 92 = d2 1 + 81 = d2 82 = d2 d = BD 12 + 92 = d2 1 + 81 = d2 82 = d2 d =

  13. Are the consecutive sides AB and BC perpendicular? Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they are perpendicular! (slopes opp reciprocals) (Use the slope formula!) AB BC

  14. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) Are the consecutive sides QU and UA perpendicular? NO, they aren’t perpendicular! (slopes not opp reciprocals) (Use the slope formula!) QU UA

  15. Given quadrilateral QUADQ(-3, 1) U(1, 3) A(4, 2) D(-4, -2) Yes, they are congruent! (same lengths) (Use the distance formula!) Are the diagonals congruent? QA 72 + 12 = d2 49 + 1 = d2 50 = d2 d = UD 52 + 52 = d2 25 + 25 = d2 50 = d2 d =

  16. Do the diagonals bisect each other? Given quadrilateral ABCDA(-4, 5) B(1, 1) C(-3, -4) D(-8, 0) Yes, they bisect each other! (same midpoint) (Use the midpoint formula!) BD (-3.5, .5) AC (-3.5, .5)

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