Quadrilateral *ABCD* is displayed below.

You are watching: If abcd is a parallelogram which of the following statements is not true

Which statement around this quadrilateral is true?

A.*ABCD*is a parallelogram because opposite angles are displayed to it is in congruent.Incorrect. The angles significant are no opposite angles of the parallelogram.

B. *ABCD* is a parallelogram because when alternating interior angles room congruent, lines space parallel, *AB* // *CD* and *AC* // *BD*.Correct!

C. *ABCD* is a rhombus since *AB* ≅ *CD* and *AC* ≅ *BD*.Incorrect. Opposite sides that space congruent room not enough to display that a square is a rhombus.

D. *ABCD* is a rectangle since *m*∠*CAD* = *m*∠*BDA.*Incorrect. These angles are marked congruent, and congruent angles have actually equal measures, however that is not adequate to present that *ABCD* is a rectangle, which requires the existence of four right angles.

square *ABCD* below is a rhombus.

Which of the following statements is **not** constantly true?

A. *m*∠*ADX* = *m*∠*CBX*Incorrect. This explain is true since *AD* // *BC,* and alternating interior angles developed by a transversal intersecting 2 parallel lines room congruent.

B. *AC* ⊥ *BD*Incorrect. This declare is true because *AC* and *BD* space both diagonals that rhombus *ABCD*, and also the diagonals that a rhombus are perpendicular.

*AD*=

*CD*Incorrect. This statement is true since a rhombus has actually 4 congruent sides, and congruent sides have equal lengths.

D. *AX* = *DX*Correct! This statement may or may not it is in true. We understand that the diagonals the a rhombus space perpendicular bisectors of each other, however we perform not know that the diagonals the a rhombus space congruent.

The diagram below shows the relationship in between the areas of the library, school, store, and park in a details neighborhood.

Based on the information presented in the diagram, i beg your pardon of the complying with statements need to be true?

A. The distance from the library come the institution is the exact same as the distance from the store to the park. Correctly! We recognize that the number is a parallelogram due to the fact that both bag of opposite sides room parallel. In a parallelogram, opposite sides are likewise congruent.

B. The street from the library come the institution is the very same as the street from the library to the store. Incorrect. We just have enough information in the figure to conclude the the number is a parallelogram, no a rhombus. We carry out not understand that surrounding sides of the parallelogram are congruent.

C. The distance from the institution to the park is the same as the street from the save to the park. Incorrect. We only have sufficient information in the figure to conclude the the number is a parallelogram, no a rhombus. We do not recognize that nearby sides of the parallelogram are congruent.

D. The distance from the save to the college is the very same as the distance from the keep to the library. Incorrect. We understand that the figure is a parallelogram due to the fact that both bag of the contrary sides room parallel. We carry out not understand whether or no the diagonal line of the parallel is the same length as among the sides.

quadrilateral *ABCD* is shown in the number below.

Which of the following statements need to be true?

A. *CE* = *EB*Incorrect. We understand that *ABCD* is one isosceles trapezoid because*AB* // *CD* and also *AC* = *BD*. However, the diagonals in an isosceles trapezoid might or might not bisect every other.

B.*CB* ⊥ *AD*Incorrect. We know that *ABCD* is one isosceles trapezoid due to the fact that *AB* // *CD* and *AC* = *BD*. However, the diagonals in an isosceles trapezoid may or might not be perpendicular.

C. *BC* = *AD*Correct! We know that *ABCD* is an isosceles trapezoid due to the fact that *AB* // *CD* and *AC* = *BD*. In an isosceles trapezoid, diagonals are congruent.

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George attracted an equilateral triangle and also reflected it throughout one that its sides. What unique quadrilateral did that create and also how did the know?

A. The polygon was a square because all sides and angles of a equilateral are congruent, for this reason the sides and angles of the quadrilateral room congruent. Incorrect. The sides space congruent, however the angle steps are 120 degrees and also 60 degrees, no 90 degrees.

B. The polygon was a rhombus due to the fact that opposite angles space congruent, and all political parties of one equilateral are congruent, making all sides that the quadrilateral congruent. Correct! The definition of a rhombus is a quadrilateral with all political parties congruent.

C. The polygon was a rectangle because a triangle reflected end its sides gives two triangles, and the brand-new shapes area is 1/2*bh *+ 1/2*bh* = *bh*, the area the a rectangle.Incorrect. The triangle would have to be reflected and rotated to kind a rectangle. *A* = *bh *is the area of a parallelogram, no necessarily a rectangle.

D. The polygon is not a quadrilateral, however rather an isosceles triangle since a triangle reflect makes an additional larger triangle.Incorrect. If a scalene or isosceles best triangle were reflected over one of its sides, it would type an isosceles triangle.