Question

given: hijk is a rect - angle; hikl is a parallelogram. prove: \\( \triangle hjl \\) is isosceles.

Explanation:

Step1: Recall properties of rectangle

In rectangle \(HIJK\), \(\overline{IK}\cong\overline{HJ}\) (opposite sides of a rectangle are congruent).

Step2: Use transitive property

Since \(\overline{IK}\cong\overline{HL}\) (from parallelogram property) and \(\overline{IK}\cong\overline{HJ}\), by transitive property \(\overline{HJ}\cong\overline{HL}\).

Step3: Conclude triangle type

If two sides of a triangle (\(\overline{HJ}\) and \(\overline{HL}\) of \(\triangle HJL\)) are congruent, then the triangle is isosceles.

Answer:

Statement 5: \(\overline{HJ}\cong\overline{HL}\); Statement 6: \(\triangle HJL\) is isosceles; Reason 6: Definition of isosceles triangle (a triangle with two congruent sides is isosceles)