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Multiple choice maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

If ABCD is an isosceles trapezium, $\angle{C}$ is equal to 

  1. $\angle{B}$
  2. $\angle{A}$
  3. $90^\circ$
  4. $\angle{D}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If ABCD is a isosceles trapezium , $\angle C\quad will\quad be\quad equal\quad to\quad \angle D $
because angles on either side of the bases are same measure/size(congruent) in a isosceles trapezium.

Multiple choice maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

Square is not a

  1. rhombus

  2. rectangle

  3. trapezium

  4. parallelogram
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The definition of a square does not comply with the definition of a trapezoid. 

The definition of a trapezoid is a quadrilateral (a closed plane figure with 4 sides) with exactly one pair of parallel sides. 

On the other hand, a square is a very special kind of quadrilateral; 
A square is also a rectangle because it has two sets of parallel sides and four right angles. 
A square is also a parallelogram because its opposite sides are parallel. 
A square is always a rhombus. A rhombus is a quadrilateral with four congruent sides. If the rhombus has 4 right angles it may also be called a square. So every square is a rhombus.

Hence square is not a trapezium.

Multiple choice maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3:7:6:4 then PQRS is a

  1. rhombus

  2. parallelogram

  3. trapezium

  4. kite
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the ABCD is a quadrilateral witch $\angle A, \angle B,\angle Cand \angle D$ in ratio  3:7:6:4

Sum of ratio 3+7+6+4=20
$\angle A+ \angle B+\angle C + \angle D=360^{0}$
$\therefore \angle A=\frac{3}{20}\times 360=54^{0}$
$\therefore \angle B=\frac{7}{20}\times 360=126^{0}$
$\therefore \angle c=\frac{6}{20}\times 360=108^{0}$
$\therefore \angle D=\frac{4}{20}\times 360=72^{0}$
Then  ABCD is a quadrilateral is trapezium

Multiple choice maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

In a trapezium  $A B C D , A B |D C$  and  $D C = 2 A B .EF$  drawn parallel to  $AB$  cuts $AD$  in  $F$  and  $B C$  in E such that $ \dfrac { BE }{ EC } =\dfrac { 3 }{ 4 } $ Diagonal $DB $  intersects  $ EF$  at  $G$  then $7 \mathrm { FE } = 10 \mathrm { AB } .$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the properties of similar triangles formed by the parallel lines in the trapezium, the ratio holds true.

Multiple choice maths construction of quadrilaterals trapeziums and kites quadrilaterals and their properties closed figures

The ratio of the measures of the consecutive angles of a quadrilateral is 1:2:3:4. What type of quadrilateral is it

  1. Trapezium

  2. Kite

  3. Parallelogram

  4. Rectangle
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of angles in a quadrilateral is 360 degrees. If the ratio is 1:2:3:4, the angles are 36, 72, 108, and 144 degrees. Since one pair of consecutive angles (72+108) sums to 180, it is a trapezium.