Figures in the Coordinate Plane (Sec 9-1) — Unit test Answers

A corner of a rectangle is cut, creating a trapezoid.

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.

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.

A carpenter cuts the corners of a rectangle to make the trapezoid shown.

Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD.

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?

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

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

On a coordinate plane, square A B C D is shown. Point A is at (3, 4), point B is at (2, negative 2), point C is at (negative 4, negative 1), and point D is at (negative 3, 5).

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.

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)°

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (5, 1), point Q is at (6, 4), point R is at (3, 10), and point S is at (2, 7).

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?

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