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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Geometry
3.8 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)

Q 1: A quadrilateral becomes a rhombus, when all its sides are equal.
False
true

Q 2: Each diagonals of a rhombus divides it into two __________.
congruent triangles
right angled triangles
similar triangles

Q 3: The diagonals of rhombus ABCD intersect at O. Given that measure of angle BAC is 530 and DO = 8, Find the measure of angle ABO.

Answer:

Q 4: The length of each side of the rhombus shown is ____.

4
3
12

Q 5: The two adjacent angles of a rhombus have degree measures 60 and 30.
True
False

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

Q 7: The value of side DC if side AB is given by 12.5 cm, is __________.

7.5 cm
11 cm
15 cm

Q 8: One of the diagonals of a rhombus is given by 10 cm. Then it divides the rhombus into two __________.
halves is 5 cm each
perpendicular bisectors
congruent triangles

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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