Chapter 5
Geometry
Mr. McKendrick
Name: ______________________
Date: _______________________
Period: ______________________
Always, Sometimes, Never Practice
Write if the statement is always, sometimes, or never true.
1.
Opposite angles of an isosceles trapezoid are supplementary.
2.
The consecutive sides of a parallelogram are congruent.
3.
The diagonals of a rectangle bisect the angles.
4.
Exactly one pair of opposite sides of a trapezoid is congruent.
5.
All angles of a parallelogram are congruent.
6.
Exactly one pair of opposite sides of a trapezoid is parallel.
7.
All sides of a kite are congruent.
8.
All angles of a trapezoid are congruent.
9.
The diagonals of square are perpendicular bisectors of each other.
10.
A rectangle is a kite.
11.
A rhombus is a square.
12.
A trapezoid is a rhombus.
13.
A square is a parallelogram.
14.
All four sides of a parallelogram are congruent.
15.
If one diagonal of a quadrilateral is the perpendicular bisector of the other, then the
quadrilateral is a rhombus.
16.
If the diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle.
17.
If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the
quadrilateral is a trapezoid.
18.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Always, Sometimes, Never Solutions
1.
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15.
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18.
Opposite angles of an isosceles trapezoid are supplementary. A
Since the lower base angles are congruent and the upper base angles are congruent, any pair
of opposite angles are supplementary.
The consecutive sides of a parallelogram are congruent. S
The consecutive sides are congruent only if the parallelogram is a rhombus (or a square).
The diagonals of a rectangle bisect the angles. S
Diagonals bisecting angles is a property of a rhombus, so this would only happen if the
rectangle was a square.
Exactly one pair of opposite sides of a trapezoid is congruent. S
This would only happen if the trapezoid was an isosceles trapezoid.
All angles of a parallelogram are congruent. S
This would only happen if the parallelogram was a rectangle (or a square).
Exactly one pair of opposite sides of a trapezoid is parallel. A
This is the definition of a trapezoid.
All sides of a kite are congruent. S
This would only happen if the kite was a rhombus.
All angles of a trapezoid are congruent. N
If all of the angles in a quadrilateral were congruent, the figure would be a rectangle. But a
trapezoid can’t be a rectangle.
The diagonals of square are perpendicular bisectors of each other. A
This is a property of a rhombus, so it would also be a property of a square.
A rectangle is a kite. S
A rectangle can be a kite…when the kite is a rhombus. A rectangle is a kite when the rectangle
is a square.
A rhombus is a square. S
A rhombus can be a square, but it doesn’t have to be.
A trapezoid is a rhombus. N
A trapezoid can’t be a rhombus because a rhombus is a parallelogram. A trapezoid can’t be a
parallelogram.
A square is a parallelogram. A
A square is a type of rectangle, which is a type of parallelogram.
All four sides of a parallelogram are congruent. S
All four sides can be congruent (it would be a rhombus), but they don’t have to be.
If one diagonal of a quadrilateral is the perpendicular bisector of the other, then the
quadrilateral is a rhombus. S
This proves that the figure is a kite. But a rhombus is a type of kite, so this is sometimes.
If the diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle. S
If the diagonals are congruent, then the quadrilateral can be a rectangle, square, or isosceles
trapezoid.
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the
quadrilateral is a trapezoid. N
This proves that a quadrilateral is a parallelogram, and a parallelogram can’t be a trapezoid.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A
This is one of the ways to prove a quadrilateral is a parallelogram.