Chapter 5: Q4 (page 187)

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

Short Answer

Expert verified

Property	Parallelogram	Rectangle	Rhombus	Square
A diag. forms two $≅$ $Δ s$ .	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.