Question

Which reasons can be used to fill in the numbered blank spaces?

Answer 1

Alternate Interior Angles Theorem
Alternate Interior Angles Theorem


Corresponding Angles Theorem
Corresponding Angles Theorem


Same-Side Interior Angles Theorem
Alternate Interior Angles Theorem


Same-Side Interior Angles Theorem
Corresponding Angles Theorem

Answer 2

2. The figure below shows a parallelogram ABCD. Side AB is parallel to side DC, and side AD is parallel to side BC:

A quadrilateral ABCD is shown with the two pairs of opposite sides AD and BC and AB and DC marked parallel . The diagonal are labeled BD and AC

A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal:

For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by SAS postulate. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC.

Which statement best describes a flaw in the student's proof?

Angle ADB is congruent to angle CBD because they are vertical angles.

Angle ADB is congruent to angle CBD because they are corresponding angles.

Triangles ABD and CDB are congruent by SSS postulate.

Triangles ABD and CDB are congruent by SAS postulate.

Answer 3

@dan815

@nincompoop

Answer 4

4. The figure below shows a parallelogram ABCD. Side AB is parallel to side DC, and side AD is parallel to side BC:

A quadrilateral ABCD is shown with the two pairs of opposite sides AD and BC and AB and DC marked parallel . The diagonal are labeled BD and AC

A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal:

For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by SAS postulate. Therefore, AB is congruent to DC and AD is congruent to BC by CPCTC.

Which statement best describes a flaw in the student's proof?

Angle ADB is congruent to angle CBD because they are vertical angles.

Angle ADB is congruent to angle CBD because they are corresponding angles.

Triangles ABD and CDB are congruent by SSS postulate.

Triangles ABD and CDB are congruent by SAS postulate.

Answer 5

@ganeshie8