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Grade 7 - Mathematics
8.8 Rhombus



Properties of Rhombus:

  1. The diagonals in a rhombus bisect each other.
  2. Each diagonal of a rhombus divides it into two congruent triangles.
  3. Opposite angles of a rhombus are equal and the sum of any two adjacent angles is 180.
  4. In a rhombus the diagonals bisect each other at right angles, that is, the diagonals are perpendicular to each other and bisect each other.

THEOREMS
  • A quadrilateral is a rhombus, if and only if it has four congruent sides.

    AB @ BC @ CD @ DA
  • A parallelogram is a rhombus, if and only if its diagonals are perpendicular

    AC ^ BD
  • A parallelogram is a rhombus, if and only if each diagonal bisects a pair of opposite angles.


Directions: Read the above review points carefully and answer the following questions:
  1. Explain the different theorems of a rhombus, in your own words, with examples.
  2. Illustrate each of the above review points by drawing different rhombus.
  3. If one of the angles of a rhombus is 2 times the adjacent angle, then what will be the value of the angle opposite to it? Give reasons.
  4. A side of a rhombus is given by 16 cm. What will be the value of half of the other side? Give reasons.
  5. Question: The diagonals of rhombus ABCD intersect at O. Given that measure of BAC is 530 and DO = 8, Find the mABO, mABC, mBCO, mBCD, mCDO, mCDA, mAOB, mBOC, mAOD, AO, AC, BD
    (Hint: Use pythagorean theorem to find the measures of angles)


Name: ___________________

Date:___________________

Grade 7 - Mathematics
8.8 Rhombus

Q 1: The two adjacent angles of a rhombus have degree measures 60 and 30.
True
False

Q 2: The length of each side of the rhombus shown is ____.

3
4
12

Q 3: A quadrilateral becomes a rhombus, when all its sides are equal.
true
False

Q 4: The opposite sides of a rhombus are given by 6 cm, 6 cm and 8 cm. Then the third side will be __________.
8 cm
6 cm
12 cm

Q 5: One of the diagonals of a rhombus is given by 10 cm. Then it divides the rhombus into two __________.
perpendicular bisectors
congruent triangles
halves is 5 cm each

Q 6: The diagonals of a rhombus bisect at __________.
right angles
acute angles
obtuse angles

Q 7: Each diagonals of a rhombus divides it into two __________.
congruent triangles
similar triangles
right angled triangles

Q 8: The value of E in the given rhombus is __________.

45
90
60

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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