Download Geometry G.9 Rhombus, Rectangle, Square, Trapezoid, Kite WS

Geometry G.9 Rhombus, Rectangle, Square, Trapezoid, Kite WS
Name: ________________________________________ Date: __________________ Block: _______
Decide whether the statement is true or false. Decide whether the converse is true or false.
If both statements are true, write a biconditional statement.
1) If a quadrilateral is a rectangle, then it is a parallelogram.
2) If a quadrilateral is a parallelogram then it is a rhombus.
3) If a quadrilateral is a square, then it is rhombus.
4) If a quadrilateral is a rectangle, then it is a rhombus.
5) If a rhombus is a square, then it is a rectangle.
In the diagram shown, BDEG is a rectangle, ABCD is a
rhombus, and GDE  63 . Find the measure of the angles.
6) GDB
7) ABC
8) DAB
9) BCG
10) GCE
11) DEG
12) AHB
13) DGB
Classify the quadrilateral (explain why). Then find the values of x and y.
14)
15)
Find the indicated measure for the figure.
16) PQRS is a rhombus.
Find mQPR , mQTP ,
RP, and QT.
17) WXYZ is a rectangle.
XZ=12. Find mWXZ ,
mWPX , PY, and WX .
18) DEFG is a square. Find
mGHF , mDGH , HF,
and DE .
19) The diagonals of rhombus ABCD form several triangles. Using a two-column proof,
prove that BFA  DFC .
Given: ABCD is a rhombus
Prove: BFA  DFC
Geometry G.9 Rhombus, Rectangle, Square, Trapezoid, Kite WS Page 2
Points A, B, C, and D are the vertices of a quadrilateral. Determine whether ABCD is a
trapezoid.
20) A(-2, 3), B(3, 3), C(-1, -2), D(2, -2)
21) A(-3, 2), B(3, 0), C(4, 3), D(-2, 5)
Quadrilateral ABCD is a trapezoid with midsegment EF .
22) If mB  73 then mC  ?
23) If mA  51 and mC  105 then mD  ?
24) If AB = 28 and DC = 13, then EF = ?
25) If EF = x + 5 and DC + AB = 4x+6, then EF = ?
The figures below are kites. Find the measures of the missing angles.
26)
27)
Use the Pythagorean theorem to find the side lengths of the kite in simplest radical form.
28)
Find the value of x.
30)
29)
31)
32)
33) You cut a piece of fabric in the shape of a kite so that the congruent angles of the kite
are 100 . Of the remaining two angles, one is 4 times larger than the other. What is the
measure of the largest angle in the kite?