Question

1 an interior designer is creating a quadrilateral coffee table with vertices at a(0, 0), b(0, 2), c(8, - 2) and d(8, - 4). which property can prove that the table is a parallelogram? a diagonals are congruent b all angles are right angles c opposite sides are congruent d opposite sides are perpendicular 2 based on the vertical angles conjecture, if ∠asc = 45°, what is the measure of ∠bed? a 45° b 90° c 60° d 30° 3 in which type of proof are statements and reasons presented side - by - side? a paragraph proof b indirect proof c two - column proof d flowchart proof 4 which property is true of all parallelograms? a diagonals bisect each other b diagonals are congruent c opposite sides are perpendicular d all angles are right angles 5 in parallelogram abcd, diagonals ac and bd intersect at point e. if ∠dac = 75°, what is the measure of ∠bca? a 60° b 75° c 45° d 90° 6 in a trapezoid, the measures of the consecutive angles next to the longer base are ____ a complementary b perpendicular c supplementary d congruent 7 according to the perpendicular bisector conjecture, what can be said about any point on the perpendicular bisector of a segment? a it divides the segment into equal parts b it is equidistant from the two endpoints of the segment c it forms congruent angles with the segment

Explanation:

1. One of the properties of a parallelogram is that opposite sides are congruent. This helps prove a quadrilateral is a parallelogram.
2. Vertical - angles are congruent. So if one vertical - angle measures 45°, the other measures 45°.
3. In a two - column proof, statements and reasons are presented side by side.
4. A property true for all parallelograms is that diagonals bisect each other.
5. In a parallelogram, alternate interior angles are congruent. So if ∠DAC = 75°, then ∠BCA=75°.
6. In a trapezoid, the measures of the consecutive angles next to the longer base are supplementary.
7. Any point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.

Answer:

1. c. Opposite sides are congruent
2. a. 45°
3. c. Two - column proof
4. a. Diagonals bisect each other
5. b. 75°
6. c. supplementary
7. b. It is equidistant from the two endpoints of the segment