Asked by kino
There are five ways to confirm that a quadrilateral is a parallelogram.
If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram.
If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
If the diagonals bisect each other, then the quadrilateral is a parallelogram.
If one pair of sides is both congruent and parallel, then the quadrilateral is a parallelogram.
(6 points)
Use the diagram to complete the following statements. When inputting answers use the proper math notation by selecting the Geometry keypad ( ∠ ); located above the number pad, to indicate that segments, angles, and triangles are used.
If AB¯¯¯¯¯¯¯¯≅
, and BC¯¯¯¯¯¯¯¯≅
, then ABCD is parallelogram.
If m∠A+m∠B=
, and m∠
+ m∠D=180
, then ABCD is parallelogram.
If ∠A≅∠
, and ∠
≅∠D
, then ABCD is parallelogram.
If AE¯¯¯¯¯¯¯¯≅
, and BE¯¯¯¯¯¯¯¯≅
, then ABCD is parallelogram.
If BC¯¯¯¯¯¯¯¯≅
, and BC¯¯¯¯¯¯¯¯∥
, then ABCD is parallelogram.
If CD¯¯¯¯¯¯¯¯≅
, and CD¯¯¯¯¯¯¯¯∥
, then ABCD is parallelogram.
If both pairs of opposite sides are parallel, then the quadrilateral is a parallelogram.
If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.
If the diagonals bisect each other, then the quadrilateral is a parallelogram.
If one pair of sides is both congruent and parallel, then the quadrilateral is a parallelogram.
(6 points)
Use the diagram to complete the following statements. When inputting answers use the proper math notation by selecting the Geometry keypad ( ∠ ); located above the number pad, to indicate that segments, angles, and triangles are used.
If AB¯¯¯¯¯¯¯¯≅
, and BC¯¯¯¯¯¯¯¯≅
, then ABCD is parallelogram.
If m∠A+m∠B=
, and m∠
+ m∠D=180
, then ABCD is parallelogram.
If ∠A≅∠
, and ∠
≅∠D
, then ABCD is parallelogram.
If AE¯¯¯¯¯¯¯¯≅
, and BE¯¯¯¯¯¯¯¯≅
, then ABCD is parallelogram.
If BC¯¯¯¯¯¯¯¯≅
, and BC¯¯¯¯¯¯¯¯∥
, then ABCD is parallelogram.
If CD¯¯¯¯¯¯¯¯≅
, and CD¯¯¯¯¯¯¯¯∥
, then ABCD is parallelogram.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To complete the statements based on the properties of a parallelogram, we can fill in the information as follows:
1. If \( AB \cong CD \), and \( BC \cong AD \), then ABCD is a parallelogram.
2. If \( m\angle A + m\angle B = 180^\circ \), and \( m\angle C + m\angle D = 180^\circ \), then ABCD is a parallelogram.
3. If \( \angle A \cong \angle C \), and \( \angle B \cong \angle D \), then ABCD is a parallelogram.
4. If \( AE \cong BE \), and \( DE \cong CE \), then ABCD is a parallelogram (assuming AE and BE are segments that cut the diagonal of the quadrilateral).
5. If \( BC \cong AD \), and \( BC \parallel AD \), then ABCD is a parallelogram.
6. If \( CD \cong AB \), and \( CD \parallel AB \), then ABCD is a parallelogram.
Just replace \( AB \), \( CD \), \( BC \), \( AD \), or their corresponding angle notations with any specified values from your diagram if needed.
1. If \( AB \cong CD \), and \( BC \cong AD \), then ABCD is a parallelogram.
2. If \( m\angle A + m\angle B = 180^\circ \), and \( m\angle C + m\angle D = 180^\circ \), then ABCD is a parallelogram.
3. If \( \angle A \cong \angle C \), and \( \angle B \cong \angle D \), then ABCD is a parallelogram.
4. If \( AE \cong BE \), and \( DE \cong CE \), then ABCD is a parallelogram (assuming AE and BE are segments that cut the diagonal of the quadrilateral).
5. If \( BC \cong AD \), and \( BC \parallel AD \), then ABCD is a parallelogram.
6. If \( CD \cong AB \), and \( CD \parallel AB \), then ABCD is a parallelogram.
Just replace \( AB \), \( CD \), \( BC \), \( AD \), or their corresponding angle notations with any specified values from your diagram if needed.
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