Quadrilaterals and Polygons: Trapezoids and Kites

think icon Think & Click: Properties of Kites

 

Now, you try. Complete the Think & Click activity by looking at the problem below, thinking about it, and then clicking on the question to reveal the solution.

 

Quadrilateral PQRS is a kite. Find the measure of angle Q.
Kite PQRS with congruent angle Q and S, angle P measures 135 degrees and angle R measures 53 degrees

 

Angles S and Q are congruent. Sum of all angles is 360.

135 + 53 + x + x = 360

188 + 2x = 360

2x = 172

x = 86

the measure of angle Q equals 86 degrees
 

Given kite EFGH has side EF with length 5 and EH with length 5. If side FG has length 10x + 5 and GH has length 2x + 27, find the value of x.
 

FG is congruent to GH

10x + 5 = 2x + 27

10x = 2x + 22

8x = 22

x = 2.75
 

If kite TUVW has diagonal TV with length 22 and segment UC with length 15, find the length of side TU.
Kite FGHI, with congruent angles F and H, diagonals intersect at point C, side FG measures 12 and segment GC measures 9

 

one-half the quantity TV equals one-half the quantity 22 equals 11

Triangle TCU is a right triangle.
TC2 + UC2 = TU2
112 + 152 = TU2
121 + 225 = TU2
346 = TU2
TU = 18.60
 

Find the length of FH in kite FGHI. Segment FG measures 12 and segment GC measures 9.
Kite FGHI, with congruent angles F and H, diagonals intersect at point C, side FG measures 12 and segment GC measures 9


FC2 + GC2 = FG2

FC2 + 92 = 122

FC2 + 81 = 144

FC2 = 63

FC = 7.94

FH = 2(FC) = 2(7.94) = 15.88