Special Parallelograms — Unit test Answers

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees.

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons1.ABCD is a square1.given2.∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles2.definition of a square3.∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA3.right angles are congruent4.AB ≅ BC ≅ CD ≅ DA4.?5.△BAD ≅ △ABC5.SAS6.BD ≅ AC6.CPCTCWhat is the missing reason in the proof?

Given: RT ≅ TV and ST ≅ TUProve: RSVU is a parallelogram. Statements Reasons1.RT ≅ TV; ST ≅ TU1.given2.∠RTS and ∠VTU are vert. ∠s;∠RTU and ∠VTS are vert. ∠s2.definition of vertical angles3.∠RTS ≅ ∠VTU;∠RTU ≅ ∠VTS3.vertical angles are congruent4.?4.SAS congruency theorem5.∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV5.CPCTC6.∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles6.definition of alternate interior angles7.RS ∥ UV and RU ∥ SV7.converse of the parallelogram diagonal theorem8.RSVU is a parallelogram8.definition of parallelogramWhat is the missing statement in step 4?

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.

In parallelogram WXYZ, WY = 12 in., XZ = 16 in., WX = 10 in., and XY = 9 in.

Rhombus LMNO is shown with its diagonals.

The angle measures of quadrilateral RSTU are shown.m∠R = (2x)°m∠S = (3x – 35)°m∠T = (x + 35)°

In parallelogram RSTU, SW = 4 cm, WT = 6 cm, RS = 5 cm, and ST = 7 cm.

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°.What are the two different angle measures of the parallelogram-shaped tile?

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. A third side measures (2n + 3) cm.What are the lengths of two adjacent sides of the parallelogram?

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.

Figure ABCD is a parallelogram.