Conditions for Parallelograms

Fill in the missing reason for the proof.

• Opposite angles are congruent.

• Alternate interior angles formed by parallel lines are congruent.

• Vertical angles are congruent.

• CPCTC

Choose the correct missing reasons for the proof.

• 4) CPCTC; 6)All quads are parallelograms

• 4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

• 4)CPCTC; 6)Definition of parallelogram

• 4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

Is this a parallelogram? How do we know?

• yes,opposite sides are congruent

• no we can not prove it is a parallelogram

• yes, one pair of sides are congruent and parallel

• yes, opposite sides are parallel

• yes, diagonals bisect each other

Answer explanation

Determine whether the figure is a parallelogram. If so, state the reason.

• Yes, quadrilateral with 2 pairs of opposite sides ≅

• Yes, quadrilateral with 2 pairs of opposite angles ≅

• Yes, quadrilateral with diagonals bisecting each other

• not a parallelogram

To prove that the following parallelogram ABCD is a rectangle, which of the following must not be true?

• AC≠DB

• AD≅BC

• m∠C=90

• ∠A≅∠B≅∠C≅∠D

Prove that if a quadrilateral is a parallelogram, then the opposite sides are congruent.

• parallel

• Alternate Interior Angles Theorem.

• Reflexive Property.

• ASA≅

• Corresponding Parts of Congruent Triangles are Con

What is the value of x?

• 132

• 66

• 114

• 48

Prove that if a quadrilateral is a parallelogram, then the opposite sides are congruent.

• parallel

• Alternate Interior Angles Theorem.

• Reflexive Property.

• ASA≅

• Corresponding Parts of Congruent Triangles are Con

Is this a parallelogram

• Yes, both pairs of opposite sides are parallel

• Yes, both pairs of opposite sides are congruent

• Yes, both pairs of opposite angles are congruent

• Yes, one pair of sides is both congruent and parallel

• No

Find the value of x that makes the quadrilateral a parallelogram.

• 29

• 42

• 78

• 11