Special Parallelograms Answers

ABCD is a square.

The figure is a parallelogram. One diagonal measures 28 units.

Which measures are true for the quilt piece? Select three options.

Which statements are true of all squares? Select three options.The diagonals are perpendicular.The diagonals are congruent to each other.The diagonals bisect the vertex angles.The diagonals are congruent to the sides of the square.The diagonals are twice the length of one side of the square.

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches.

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus. Statements Reasons1.ABCD is a parallelogram1.given2.∠AMB, ∠BMC, ∠CMD, and ∠DMA are right angles2.given3.∠AMB ≅ ∠BMC ≅ ∠CMD ≅ ∠DMA3.right angles are congruent4.AC bisects BD; BD bisects AC;4.diagonals of a parallelogram bisect each other5.AM ≅ MC, MB ≅ MD5.definition of a bisector6.?6.SAS congruency theorem7.AB ≅ BC ≅ CD ≅ DA7.CPCTC8.figure ABCD is a rhombus8.definition of a rhombus

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

The figure shown is a rhombus.

Consider the diagram and proof below.Given: WXYZ is a parallelogram, ZX ≅ WYProve: WXYZ is a rectangle Statement Reason1.WXYZ is a ▱; ZX ≅ WY1.given2.ZY ≅ WX2.opp. sides of ▱ are ≅3.YX ≅ YX3.reflexive4.△ZYX ≅ △WXY4.SSS ≅ thm.5.∠ZYX ≅ ∠WXY5.CPCTC6.m∠ZYX ≅ m∠WXY6.def. of ≅7.m∠ZYX + m∠WXY = 180°7.?8.m∠ZYX + m∠ZYX = 180°8.substitution9.2(m∠ZYX) = 180°9.simplification10.m∠ZYX = 90°10.div. prop. of equality11.WXYZ is a rectangle11.rectangle ∠ thm.What is the missing reason in Step 7?

Rectangle T R E C is shown. Diagonals are drawn from point R to point C and from point E to point T and intersect in the middle. The distance from point R to the middle is 2 x minus 3 and the distance from the middle point to point C is x + 7.