1) Answer with “always”, “sometimes”, or “never”.
a) All four interior angles of an isosceles trapezoid can be congruent.
b) The diagonals of a trapezoid to intersect at \(90^{\circ}\) angles.
c) A kite can have all four sides congruent.
d) The five properties of a parallelogram apply to an isosceles trapezoid.
e) The diagonals of a trapezoid are congruent.
f) The opposite angles of an isosceles trapezoid are congruent.
g) A square is both a trapezoid and a kite.
h) The diagonals of an isosceles trapezoid bisect their interior angles.
i) One diagonal of a trapezoid divides the figure into two congruent triangles.
j) An isosceles trapezoid has opposite angles supplementary.
k) A kite can have three of its interior angles all \(91^{\circ}\).
l) A trapezoid can be a parallelogram.
m) A kite is a figure with exactly two pairs of consecutive sides congruent.
n) The upper base angles of a trapezoid are supplementary.
o) The angles of a parallelogram are bisected by the diagonals.
p) A rectangle is a kite.
a) All four interior angles of an isosceles trapezoid can be congruent.
b) The diagonals of a trapezoid to intersect at \(90^{\circ}\) angles.
c) A kite can have all four sides congruent.
d) The five properties of a parallelogram apply to an isosceles trapezoid.
e) The diagonals of a trapezoid are congruent.
f) The opposite angles of an isosceles trapezoid are congruent.
g) A square is both a trapezoid and a kite.
h) The diagonals of an isosceles trapezoid bisect their interior angles.
i) One diagonal of a trapezoid divides the figure into two congruent triangles.
j) An isosceles trapezoid has opposite angles supplementary.
k) A kite can have three of its interior angles all \(91^{\circ}\).
l) A trapezoid can be a parallelogram.
m) A kite is a figure with exactly two pairs of consecutive sides congruent.
n) The upper base angles of a trapezoid are supplementary.
o) The angles of a parallelogram are bisected by the diagonals.
p) A rectangle is a kite.
3) The measure of one of the angles of an isosceles trapezoid \(RAIN\) is \(3.54^{\circ}\) less than half the measure of another. If \(m\angle R\) is less than \(m\angle A\), find the measure of \(\angle I\) to the nearest second.
4) \(KITE\) is a kite. \(KI = 9\), \(IT = x^2\), and \(TE = 6x + 7\). Find all possible perimeters of the kite.
5) \(BIKE\) is a kite. But Suzy and Ralphie can’t agree on which sides are congruent. Suzy says \(\overline{BE} \cong\overline{EK}\) and Ralphie argues that \(\overline{EK} \cong \overline{IK}\). \(BE = 15 + 4x\), \(KE = 3x + 21\) and \(IK = 7 - 4x\). Use your mathematical expertise to help Suzy and Ralphie settle their disagreement.
4) \(KITE\) is a kite. \(KI = 9\), \(IT = x^2\), and \(TE = 6x + 7\). Find all possible perimeters of the kite.
5) \(BIKE\) is a kite. But Suzy and Ralphie can’t agree on which sides are congruent. Suzy says \(\overline{BE} \cong\overline{EK}\) and Ralphie argues that \(\overline{EK} \cong \overline{IK}\). \(BE = 15 + 4x\), \(KE = 3x + 21\) and \(IK = 7 - 4x\). Use your mathematical expertise to help Suzy and Ralphie settle their disagreement.
7) Using Desmos or GeoGebra, prove that one diagonal of a kite divides it into 2 congruent triangles, while the other diagonal divides it into two isosceles triangles.
9) \(EFGH\) is a kite. \(EF = 3x + 4y\), \(FG = 2x + 20\), \(EH = 12\), and \(HG = x + 2y\). Find the perimeter of the kite.
10) \(ABCD\) is a kite. \(AB = 9\), \(BC = x^2\), and \(CD = 6x + 7\). Find all possible perimeters of the kite.
11) Answer with “Always”, “Sometimes”, or “Never” true.
a) A trapezoid is a parallelogram
b) A trapezoid is a kite
c) A kite is a rhombus
d) The diagonals of a trapezoid bisect each other.
e) Lower base angles of a trapezoid are supplementary.
f) Consecutive angles of a trapezoid are supplementary.
g) A quadrilateral is a trapezoid.
h) A kite is a square.
i) A parallelogram is a kite.
12) Research: A four sided figure with one pair of opposite sides parallel is only called a trapezoid around the world.
10) \(ABCD\) is a kite. \(AB = 9\), \(BC = x^2\), and \(CD = 6x + 7\). Find all possible perimeters of the kite.
11) Answer with “Always”, “Sometimes”, or “Never” true.
a) A trapezoid is a parallelogram
b) A trapezoid is a kite
c) A kite is a rhombus
d) The diagonals of a trapezoid bisect each other.
e) Lower base angles of a trapezoid are supplementary.
f) Consecutive angles of a trapezoid are supplementary.
g) A quadrilateral is a trapezoid.
h) A kite is a square.
i) A parallelogram is a kite.
12) Research: A four sided figure with one pair of opposite sides parallel is only called a trapezoid around the world.