Special Quadrilaterals Geometry

Construct a square ABCD of side 6.3 cm. The length of diagonal AC is ____

• 8.9 cm

• 12.5 cm

• 6.3 cm

• 12.6 cm

Answer explanation

Let's construct square ABCD with length of side 6.3 cm Step I: Draw AB = 6.3 cm Step II: All angles of a square are right angles. So, draw a line XY perpendicular to AB at B Step III: With B as center draw an arc of radius 6.3cm which intersects XY at point C such that BC = 6.3 cm. Step IV: Draw a perpendicular UV to BC at C. Step V: With C as center draw an arc of radius 6.3cm which intersects UV at point D such that CD = 6.3 cm such that CD = 6.3 cm Step VI: Join points A and D. Square ABCD is constructed. Step VII: Measure the length of the diagonal AC It will come out to be 8.9 cm

Construct a rectangle MOST such that length of adjacent sides is 4.8 cm and 5.5 cm, given that MO < OS. What will be the length of its diagonals?

• 8.3 cm

• 7.3 cm

• 5 cm

• 8 cm

Answer explanation

In rectangle MOST since MO < OS therefore the measure of MO = 4.8 cm and the measure of OS = 5.5 cm. Let's construct a rectangle MOST Step I: Draw MO = 4.8 cm Step II: All angles of a rectangle are right angles. So, draw a line PQ perpendicular to MO at O Step III: With O at center, draw an arc of radius 5.5 cm which intersects MO at point S such that OS = 5.5 cm. Step IV: Draw a perpendicular UV to OS at point S. Step V: With S at center, draw an arc of radius 4.8cm which intersects UV at point T such that MO = ST = 4.8 cm Step VI: Join points M and T. Thus rectangle MOST is constructed. Step VII: Join MS and measure the value of diagonal MS. It comes out to be 7.3 cm and the diagonals of a rectangle are equal. The correct answer is option 2.

A rhombus's sides are 1) ____________ and it's diagonals are 2)____________

• 1) congruent

  2) perpendicular

• 1) congruent

  2) congurent

• 1) perpendicular

  2) congruent

• 1) congruent

  2) congruent and perpendicular

A square's sides are 1) ____________ and it's diagonals are 2)____________

• 1) congruent

  2) perpendicular

• 1) congruent

  2) congurent

• 1) perpendicular

  2) congruent

• 1) congruent and perpendicular

  2) congruent and perpendicular

How do you show diagonals are perpendicular?

• They would have opposite reciprocal slopes

• They would have the same slope

• They would have the same midpoint

• They would look perpendicular

The diagonals of a rectangle are

• perpendicular

• congruent

• perpendicular and congruent

• parallel and congruent

The diagonals of a rhombus are _________.

• Perpendicular and bisected

• Perpendicular

• Bisected

• Congruent

Parallelograms, recatangles, rhombus and squares ALL share what properties of diagonals?

• congruent

• perpendicular

• bisected

• parallel

Which special quadrilaterals have perpendicular diagonals?

• parallelogram and rectangle

• square and rhombus

• rectangle and square

• rhombus and parallelogram

Which option could be used to prove a quadrilateral is a parallelogram?

• Both pairs of opposite sides are congruent

• Diagonals are congruent

• One pair of opposite sides are congruent

• Both pairs of opposite sides are congruent and diagonals are congruent