Chapter 5.4, Problem 2PSA

a.

To determine

To find:The statement opposite sides of a kiteKITEare congruent is true.

Answer to Problem 2PSA

The statementopposite sides are congruent is false.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals ofkiteKITEare KTand IE.

  

Two disjoints pairs of consecutive sides are congruent.

  $\begin{array}{l}\overline{IT}\cong \overline{ET}\\ \overline{KI}\cong \overline{KE}\end{array}$

b.

To determine

To find: The statement opposite sides of a kite KITEare parallel is true.

Answer to Problem 2PSA

The statement opposite sides are parallel is false.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals of kite KITEare KT and IE.

  

A kite has got two pairs of sides next to each other that have equal length but none of the sides are parallel.

c.

To determine

To find:The statement diagonals KTand IE of a kite KITE bisect the angles is true.

Answer to Problem 2PSA

The statement diagonals KT and IEbisect the angles is true.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals of kite KITEare KT and IE.

  

If a quadrilateral is kite, it has one diagonal that bisects a pair of opposite angles.

d.

To determine

To find:The statement diagonals KT and IE of a kite KITEbisect each other is true.

Answer to Problem 2PSA

The statement diagonals KTand IE bisect each other is true.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals of kite KITEare KT and IE.

  

If a quadrilateral is kite, it has one diagonal that bisects the other diagonal.

Diagonals KT and IE bisect each other at point S.

e.

To determine

To find:The statement diagonals KT and IE of a kite KITEare congruent is true.

Answer to Problem 2PSA

The statement diagonals KT and IEare congruent is false.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals of kite KITEare KT and IE.

  

The consecutive sides are congruent but the diagonals are not congruent.

Diagonals KT and IEare not congruent.

f.

To determine

To find:The statement diagonals KT and IE of a kite KITE are perpendicular is true.

Answer to Problem 2PSA

The statement diagonals KT and IE are perpendicular is true.

Explanation of Solution

Given information:

A KITE with sides KI, IT, TE and KE.

Diagonals of kite KITEare KT and IE.

  

The intersection of the diagonals of a kite form right angles. This means that they are perpendicular. The longer diagonal of a kite bisects the shorter one. This means that the longer diagonal cuts the shorter one in half.