Chapter 5.4, Problem 3PSA

a.

To determine

To find:The statement opposite sides of an isosceles trapezoid RTPAare congruent is true.

Answer to Problem 3PSA

The statementopposite sides are congruent is false.

Explanation of Solution

Given information:

An isosceles trapezoidRTPA with sides RT, TP, PA and RA.

Diagonals oftrapezoid RTPA are RP and TA.

  

In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal lengths. The diagonals are of equal length. Only legs are congruent but bases are not congruent. Hence, the statement is false.

b.

To determine

To find: The statement opposite sides of an isosceles trapezoid RTPA are parallel is true.

Answer to Problem 3PSA

The statement opposite sides are parallel is false.

Explanation of Solution

Given information:

An isosceles trapezoid RTPA with sides RT, TP, PA and RA.

Diagonals of trapezoid RTPA are RP and TA.

  

In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal lengths. The diagonals are of equal length. Only bases are parallel but legs are not parallel. Hence, the statement is false.

c.

To determine

To find:The statement diagonalsRP and TAof an isosceles trapezoid RTPAbisect the anglesis true.

Answer to Problem 3PSA

The statement diagonals RP and TA bisect the angles is false.

Explanation of Solution

Given information:

An isosceles trapezoid RTPA with sides RT, TP, PA and RA.

Diagonals of trapezoid RTPA are RP and TA.

  

A diagonal doesn’t bisect angles in an isosceles trapezoid. It only happens in a square or a rhombus as there the length and breadth, both are equal.

d.

To determine

To find:The statement diagonals RP and TA of an isosceles trapezoid RTPA bisect each otheris true.

Answer to Problem 3PSA

The statement diagonals RP and TA bisect each other is false.

Explanation of Solution

Given information:

An isosceles trapezoid RTPA with sides RT, TP, PA and RA.

Diagonals of trapezoid RTPA are RP and TA.

  

Isosceles trapezium is a trapezium whose non parallel sides are equal. If we have a quadrilateral whose diagonals bisect each other then it happens to be parallelogram. Every parallelogram is a trapezium but every trapezium is not parallelogram.

e.

To determine

To find:The statementdiagonals RP and TA of an isosceles trapezoid RTPAare congruentis true.

Answer to Problem 3PSA

The statement diagonals RP and TAare congruent is true.

Explanation of Solution

Given information:

An isosceles trapezoid RTPA with sides RT, TP, PA and RA.

Diagonals of trapezoid RTPA are RP and TA.

  

The diagonals of an isosceles trapezoid are also congruent, but they do not bisect each other. Isosceles trapezoid diagonals theorem states that “The diagonals of an isosceles trapezoid are congruent.