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Sometimes, Always or Never

Sometimes, Always or Never. A trapezoid is a ll gram. A rhombus is a ll gram . A parallelogram is a trapezoid. 4. A rhombus is a square. 5. The diagonals of a rhombus are congruent. never always never sometimes sometimes.

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Sometimes, Always or Never

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  1. Sometimes, Always or Never • A trapezoid is a ll gram. • A rhombus is a ll gram. • A parallelogram is a • trapezoid. • 4. A rhombus is a square. • 5. The diagonals of a rhombus are congruent . never always never sometimes sometimes

  2. Given : D is the midpoint of AB E is the midpoint of BC Find: x, y and z. B D E A C 5x + 3 6z - 8 2y 3x + 15 4z + 12 50 x = 6, y = 25 and z =

  3. Given: EF = FG = GHFind x and y if AB = 2x+12,BC = 4y and CD = 7x-8 A E B F C G D H x = 4, y = 5

  4. Prove that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  5. 1 2 A B E D C 3 4 s r 1) AC and DB given bisect each other at E 2) E is the midpoint of def bisector AC and DB 3) AECE, DEBE def midpoint 4) 1  2 vertical ’s  thm. • AED  CEB SAS post. 6) AD  CB, 3  4 CPCTC 7) AD // CB alt. int ’s  lines ll 8) ABCD is a //gram one pair opp sides // &  thm.

  6. A 1 D C 2 3 B 4 5 m 2 = 70 m 3 = 70 m 4 = 140 m 5 = 20 If CD is a median and m 1 = 20 find the measures of the rest of the numbered angles.

  7. A B C D E F Find x if CD = 5x + 2, AB = x + 3 and EF = 4x + 10

  8. A 1 D C 2 3 B 4 5 m 2 = 30 m 3 = 30 m 4 = 60 m 5 = 60 Find the measure of the numbered angles if m  1 = 60.

  9. A B C D E F Find xif CD = 15, AB = 12 and EF = x

  10. Given B, C and F are midpoints of DA, AE and DE respectively. Find BC, CF and BF, if AE = 22, DE = 25 and AD = 27. A B C D F E 12.5 11 13.5

  11. Prove that if one pair of opposite sides of a quadrilateral are both congruent and parallel then the quadrilateral is a parallelogram.

  12. A B D C s r 1) AD//BC, ADBC given 2) Draw DB through any two pts. Exactly 1 line 3) ADB  CBD alt. int  ‘ s  thm. 4) DB DB reflexive prop   ‘ s 5) ABD  DCB SAS post. 6) AB  DC CPCTC 7) ABCD is a //gram both pair opp sides  thm.

  13. The segment that joins the midpoints of two sides of a triangle 1. is parallel to the third side; 2. is half as long as the third side.

  14. Find x and y 6x 10 20 10 4y 10 x = , y = 5

  15. If three parallel lines cut off congruent segments on one transversal, then they cut off_________ _________on every transversal. congruent segments

  16. Find x 4x + 5 8x - 35 x = 10

  17. If two lines are parallel, then all points on one line are _______ from the other line. equidistant

  18. What are the 5 ways to prove a quadrilateral is a parallelogram?

  19. Show that both pairs of opposite sides are parallel.Show that both pair of opposite sides are congruent.Show that one pair of opposite sides are both // and .Show that both pair of opposite angles are congruent.Show that the diagonals bisect each other.

  20. Sometimes, Always or Never • Adjacent sides of a rhombus are congruent. • Adjacent sides of a trap are congruent. • Both pair of opposite angles of a rectangle are congruent. • 4. A square is a trapezoid. always sometimes always never

  21. Name the quadrilateral by its best name:SNOW S(0, 3)N(5, 4)O(6, -1)W(1, -2) square

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