Question
The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent: According to the given information,and. Construct a diagonal from
The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent: According to the given information,and. Construct a diagonal from A to C with a straightedge. ________________. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the Alternate Interior Angles Theorem. Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Postulate. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent. Which sentence accurately completes the proof? (2 points)
Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem. | |
Diagonal BD is congruent to itself by the Reflexive Property of Equality | |
Diagonal AC is congruent to itself by the Reflexive Property of Equality. | |
Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). |
2.
(02.06 MC) The figure below shows rectangle ABCD: The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other:
Statement | Reason |
---|---|
ABCD is a rectangle. | Given |
andare parallel. | Definition of a Parallelogram |
andare parallel. | Definition of a Parallelogram |
CAD ACB | Alternate interior angles theorem |
Definition of a Parallelogram | |
ADB CBD | Alternate interior angles theorem |
ADE CBE | Angle-Side-Angle (ASA) Postulate |
CPCTC | |
CPCTC | |
bisects | Definition of a bisector |
Which statement can be used to fill in the blank space? (2 points)
3.
(02.06 MC) ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 21 and the measure of angle ADC is 125, what is the measure of angle DAC? (2 points)
73 | |
62 | |
42 | |
34 |
4.
(02.06 MC) In parallelogram EFGH, the measure of angle G is (4x + 16) and the measure of angle H is (2x 16). What is the measure of angle H? (2 points)
32 | |
44 | |
88 | |
136 |
5.
(02.06 MC) The figure shows rectangle RSTW. Which of the following conditions satisfies the criteria for rectangles? (2 points)
mSRZ = 40 | |
mSTZ = 40 | |
mSRW = 80 | |
mTWR = 80 |
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