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9.1 worksheet find the value of each variable in the parallelogram. 1. …

Question

9.1 worksheet
find the value of each variable in the parallelogram.
1.
2.
3.
4.
5.
6.
find the measure of the indicated angle in the parallelogram.

  1. find m∠c.
  2. find m∠e.
  3. find m∠k.

find the value of each variable in the parallelogram.
10.
11.
12.
use the diagram of parallelogram mnop at the right to copy and complete the statement. explain.

  1. (overline{mn}cong)?
  2. (overline{mn}parallel)?
  3. (overline{on}cong)?
  4. (angle mpocong)?
  5. (overline{pq}cong)?
  6. (overline{qm}cong)?
  7. (angle moncong)?
  8. (angle npocong)?

Explanation:

Response
  1. For problem 1 in the parallelogram:
  • In a parallelogram, opposite - sides are equal.
  • Step1: Find the value of \(x\)
  • Since opposite sides are equal, \(x = 11\).
  • Step2: Find the value of \(y\)
  • Since opposite sides are equal, \(y = 8\).
  1. For problem 2 in the parallelogram:
  • Step1: Set up equations for opposite - sides
  • For the vertical sides, \(a - 3=14\), so \(a=14 + 3=17\).
  • For the horizontal sides, \(b + 2 = 7\), so \(b=7 - 2 = 5\).
  1. For problem 3 in the parallelogram:
  • In a parallelogram, opposite angles are equal. So \(m = 161^{\circ}\).
  1. For problem 4 in the parallelogram:
  • In a parallelogram, adjacent angles are supplementary (\(A + B=180^{\circ}\)).
  • Step1: Set up the equation for adjacent angles
  • \(4r+76 = 180\).
  • Subtract 76 from both sides: \(4r=180 - 76=104\).
  • Divide both sides by 4: \(r=\frac{104}{4}=26\).
  1. For problem 5 in the parallelogram:
  • Step1: Use the property of opposite - sides
  • For the horizontal sides, \(c - 5=20\), so \(c=20 + 5 = 25\).
  • For the vertical sides, \(d + 19=68\), so \(d=68 - 19 = 49\).
  1. For problem 6 in the parallelogram:
  • Step1: Use the property of opposite - sides
  • For the vertical sides, \(2p=124\), so \(p = 62\).
  • For the horizontal sides, \(5q-4 = 49\). Add 4 to both sides: \(5q=49 + 4=53\), then \(q=\frac{53}{5}=10.6\).
  1. For problem 7 in the parallelogram:
  • In a parallelogram, opposite angles are equal. So \(m\angle C=119^{\circ}\).
  1. For problem 8 in the parallelogram:
  • In a parallelogram, adjacent angles are supplementary. If one angle is \(136^{\circ}\), then \(m\angle E=180 - 136=44^{\circ}\).
  1. For problem 9 in the parallelogram:
  • In a parallelogram, opposite angles are equal. So \(m\angle K = 78^{\circ}\).
  1. For problem 10 in the parallelogram:
  • In a parallelogram, the diagonals bisect each other.
  • Step1: Set up equations for the diagonals
  • For one part of the diagonal, \(h - 8=12\), so \(h=12 + 8 = 20\).
  • For the other part, \(g + 7=15\), so \(g=15 - 7 = 8\).
  1. For problem 11 in the parallelogram:
  • Since the diagonals bisect each other.
  • Step1: Set up equations for the diagonals
  • For one part of the diagonal, \(2y+9 = 12\), subtract 9 from both sides: \(2y=12 - 9 = 3\), then \(y=\frac{3}{2}=1.5\).
  • For the other part, \(3x + 6=27\), subtract 6 from both sides: \(3x=27 - 6 = 21\), then \(x = 7\).
  1. For problem 12 in the parallelogram:
  • Since the diagonals bisect each other.
  • Step1: Set up equations for the diagonals
  • For one part of the diagonal, \(4j+9=31\), subtract 9 from both sides: \(4j=31 - 9 = 22\), then \(j=\frac{22}{4}=5.5\).
  • For the other part, \(6j-5=7k - 4\). Substitute \(j = 5.5\) into the equation: \(6\times5.5-5=7k - 4\).
  • First, calculate \(6\times5.5-5=33 - 5 = 28\). Then the equation becomes \(28=7k - 4\). Add 4 to both sides: \(7k=28 + 4 = 32\), then \(k=\frac{32}{7}\approx4.57\).
  1. For problem 13 in the parallelogram \(MNOP\):
  • In a parallelogram, opposite sides are equal. So \(\overline{MN}\cong\overline{OP}\).
  1. For problem 14 in the parallelogram \(MNOP\):
  • In a parallelogram, opposite sides are parallel. So \(\overline{MN}\parallel\overline{OP}\).
  1. For problem 15 in the parallelogram \(MNOP\):
  • In a parallelogram, opposite sides are equal. So \(\overline{ON}\cong\overline{MP}\).
  1. For problem 16 in the parallelogram \(MNOP\):
  • In a par…

Answer:

  1. \(x = 11,y = 8\)
  2. \(a = 17,b = 5\)
  3. \(m = 161^{\circ}\)
  4. \(r = 26\)
  5. \(c = 25,d = 49\)
  6. \(p = 62,q = 10.6\)
  7. \(m\angle C=119^{\circ}\)
  8. \(m\angle E=44^{\circ}\)
  9. \(m\angle K = 78^{\circ}\)
  10. \(h = 20,g = 8\)
  11. \(x = 7,y = 1.5\)
  12. \(j = 5.5,k=\frac{32}{7}\approx4.57\)
  13. \(\overline{MN}\cong\overline{OP}\)
  14. \(\overline{MN}\parallel\overline{OP}\)
  15. \(\overline{ON}\cong\overline{MP}\)
  16. \(\angle MPO\cong\angle NOM\)
  17. \(\overline{PQ}\cong\overline{QM}\)
  18. \(\overline{QM}\cong\overline{PQ}\)
  19. \(\angle MON\cong\angle NPM\)
  20. \(\angle NPO\cong\angle OMN\)