Question

Copy the chart. Then place check marks in the appropriate spaces.

Short answer

Property	Parallelogram	Rectangle	Rhombus	Square
A diag. forms two $\cong$$\Delta s$.	yes	yes	yes	yes

Step-by-step solution

Step 1. Description of step.

A parallelogram is a quadrilateral whose opposite sides are congruent, that is they are equal in length. A diagonal of a parallelogram can be considered as a transversal intersecting two parallel sides of a parallelogram. Then the alternate interior angles formed by a transversal are equal in measure and therefore the triangles formed due to diagonal are congruent by the ASA postulate.

The rectangle is a special type of parallelogram in which opposite sides are congruent, that is they are equal in length and all the interior angles are right angles. A diagonal of a rectangle can be considered as a transversal intersecting two parallel sides of a rectangle. Then the alternate interior angles formed by a transversal are equal in measure and therefore the triangles formed due to diagonal are congruent by the ASA postulate.

Step 2. Description of step.

Rhombus is a special type of parallelogram whose opposite sides are congruent and all four sides are equal in length. A diagonal of a rhombus can be considered as a transversal intersecting two parallel sides of a rhombus. Then the alternate interior angles formed by a transversal are equal in measure and therefore the triangles formed due to diagonal are congruent by the ASA postulate.

Square is a type of parallelogram whose opposite sides are congruent and the interior angles are right angles. A diagonal of a square can be considered as a transversal intersecting two parallel sides of a square. Then the alternate interior angles formed by a transversal are equal in measure and therefore the triangles formed due to diagonal are congruent by the ASA postulate.

Step 3. Description of step.

In all the quadrilaterals, that is, parallelogram, rectangle, rhombus and square, diagonals form two congruent triangles. Therefore,

Property	Parallelogram	Rectangle	Rhombus	Square
A diag. forms two $\cong ∆\mathrm{s}$.	yes	yes	yes	yes