Question

1 select all quadrilaterals for which a diagonal is also a line of symmetry. a trapezoid c parallelogram e rectangle b isosceles trapezoid d rhombus f square 2 here is rhombus efgh. show that diagonal eg is a line of symmetry for rhombus efgh.

Explanation:

Step1: Recall properties of quadrilaterals

A line of symmetry divides a figure into two congruent parts.

Step2: Analyze trapezoid

A general trapezoid has no diagonal as a line - of - symmetry. An isosceles trapezoid has a line of symmetry but not a diagonal as a line of symmetry.

Step3: Analyze parallelogram

A general parallelogram has no line of symmetry, let alone a diagonal as a line of symmetry.

Step4: Analyze rhombus

The diagonals of a rhombus are lines of symmetry because a rhombus has all - sides equal and the diagonals bisect the angles and are perpendicular bisectors of each other.

Step5: Analyze rectangle

The diagonals of a rectangle are not lines of symmetry (a rectangle has two lines of symmetry that are the mid - point connectors of opposite sides).

Step6: Analyze square

A square is a special rhombus, and its diagonals are lines of symmetry.

for question 2:

Step1: Recall properties of a rhombus

In rhombus EFGH, all sides are equal, i.e., \(EH = EF=FG = GH\). The diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus.

Step2: Consider reflection across EG

When we reflect point H across line EG, since the diagonal EG bisects \(\angle HEF\) and \(\angle HGF\) and \(EH = EF\), \(GH=GF\), the image of point H will coincide with point F. Also, the image of point E and G will be themselves as they lie on the line of reflection EG. So, the two halves of the rhombus on either side of EG are mirror - images of each other.

Answer:

D. rhombus, F. square