Quadrilateral Proofs 2.06 FLVS (100%)
The following is an incomplete paragraph proving that the opposite sides of
parallelogram ABCD are congruent:
Parallelogram ABCD is shown where segment AB is parallel to segment DC and
segment BC is parallel to segment AD.
According to the given information, segment AB is parallel to segment DC and segment
BC is parallel to segment AD. Construct a diagonal from A to C with a straightedge. It is
congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are
congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are
congruent by the Alternate Interior Theorem. ________________. By CPCTC, opposite
sides AB and CD, as well as sides BC and DA, are congruent.
Which sentence accurately completes the proof?
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA)
Theorem.
The figure shows rhombus ABCD. Which of the following conditions satisfies the criteria
for rhombi?
Parallelogram rhombus ABCD with diagonals BD and AC intersecting at E
m∠BEC = 90°
ABCD is a parallelogram with diagonal AC. If the measure of angle DCA is 26° and the
measure of angle ABC is 113°, what is the measure of angle BCA?
Parallelogram ABCD with diagonal AC; the measure of angle ABC is 113 degrees, and
the measure of angle DCA is 26 degrees.
41°
In parallelogram EFGH, the measure of angle E is (2x + 3)° and the measure of angle F
is (3x − 33)°. What is the measure of angle E?
87°
The figure below shows rectangle ABCD:
Rectangle ABCD with diagonals AC and BD passing through point E
The following two-column proof with a missing statement proves that the diagonals of
the rectangle bisect each other:
Statement Reason
ABCD is a rectangle. Given
segment AB and segment
CD are parallel. Definition of a Parallelogram
segment AD and segment
BC are parallel. Definition of a Parallelogram
Alternate interior angles theorem
The following is an incomplete paragraph proving that the opposite sides of
parallelogram ABCD are congruent:
Parallelogram ABCD is shown where segment AB is parallel to segment DC and
segment BC is parallel to segment AD.
According to the given information, segment AB is parallel to segment DC and segment
BC is parallel to segment AD. Construct a diagonal from A to C with a straightedge. It is
congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are
congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are
congruent by the Alternate Interior Theorem. ________________. By CPCTC, opposite
sides AB and CD, as well as sides BC and DA, are congruent.
Which sentence accurately completes the proof?
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA)
Theorem.
The figure shows rhombus ABCD. Which of the following conditions satisfies the criteria
for rhombi?
Parallelogram rhombus ABCD with diagonals BD and AC intersecting at E
m∠BEC = 90°
ABCD is a parallelogram with diagonal AC. If the measure of angle DCA is 26° and the
measure of angle ABC is 113°, what is the measure of angle BCA?
Parallelogram ABCD with diagonal AC; the measure of angle ABC is 113 degrees, and
the measure of angle DCA is 26 degrees.
41°
In parallelogram EFGH, the measure of angle E is (2x + 3)° and the measure of angle F
is (3x − 33)°. What is the measure of angle E?
87°
The figure below shows rectangle ABCD:
Rectangle ABCD with diagonals AC and BD passing through point E
The following two-column proof with a missing statement proves that the diagonals of
the rectangle bisect each other:
Statement Reason
ABCD is a rectangle. Given
segment AB and segment
CD are parallel. Definition of a Parallelogram
segment AD and segment
BC are parallel. Definition of a Parallelogram
Alternate interior angles theorem
