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, BDEF 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. 17) WXYZ is a rectangle. 18) DEFG is a square. Find Find mQPR, mQTP , XZ=12. Find mWXZ , mGHF , mDGH , HF, RP, and QT. mWPX , PY, and WX . 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 mB 73 then mC ?
23) If mA 51 and mC 105then mD ?
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) 29)
Find the value of x. 30) 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?