Proving a Quadrilateral Is a Parallelogram - Assignment

In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply. - ML ∥ NO - ML ⊥ LO - LO ≅ MN - ML ≅ LO - MN ⊥ NO

- ML ∥ NO - LO ≅ MN

If quadrilateral LMNO is a parallelogram, what must the measure of angle LMN be?

105°

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

x = 3

Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO Prove: MNOL is a parallelogram. Complete the paragraph proof.We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △ ---- By CPCTC, ∠LMO ≅ ∠ ---- and ∠NMO ≅ ∠LOM. Both pairs of angles are also ---- based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram

- ONM - NOM - alternate interior angles

Given: RW ≅ WT; UW ≅ WS Prove: RSTU is a parallelogram. Identify the steps that complete the proof.

- vertical angles theorem - SAS - CPCTC

Quadrilateral RSTU has one pair of opposite parallel sides and one pair of opposite congruent sides as shown. Based on the given information, which statement best explains whether the quadrilateral is a parallelogram? A. It cannot be determined from the information given. B. It is not a parallelogram because the congruent sides cannot be parallel. C. It is not a parallelogram because the parallel sides cannot be congruent. D. It is a parallelogram based on the single opposite side pair theorem.

A. It cannot be determined from the information given.

What must the length of segment AD be for the quadrilateral to be a parallelogram? A. 8 units B. 16 units C. 31 units D. 62 units

C. 31 units

To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem. Which reasons can Travis use to prove the two triangles are congruent? Check all that apply. - ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem. - WY ≅ WY by the reflexive property. - ∠ZWY ≅ ∠XWY by the corresponding ∠s theorem. - WX ≅ ZY by definition of a parallelogram. - WZ ≅ XY by the given.

- ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem. - WY ≅ WY by the reflexive property. - WZ ≅ XY by the given.

Based on the measures shown, could the figure be a parallelogram? A. Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in. B. Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 8 in. C. No, there are three different values for x when each expression is set equal to 10. D. No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

A. Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.