Quadrilateral Proofs 2.06 FLVS (100%)

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 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°

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 Segment BC is congruent to segment AD Definition of a Parallelogram ∠ADB ≅ ∠CBD Alternate interior angles theorem ΔADE ≅ ΔCBE Angle-Side-Angle (ASA) Postulate Segment BE is congruent to segment DE CPCTC Segment AE is congruent to segment CE CPCTC Segment AC bisects segment BD. Definition of a bisector Which statement can be used to fill in the blank space?

∠CAD ≅ ∠ACB