Question
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 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
GPT-4o mini
To complete the statements regarding the quadrilateral ABCD being a parallelogram, please fill in the necessary 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 \( BE \cong CD \), then ABCD is a parallelogram.
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.
These statements leverage the properties of parallelograms, such as the conditions for sides being equal, angles being supplementary, and opposite angles being equal.
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 \( BE \cong CD \), then ABCD is a parallelogram.
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.
These statements leverage the properties of parallelograms, such as the conditions for sides being equal, angles being supplementary, and opposite angles being equal.