Question

6 multiple choice 1 point klmn is a rectangle. which statement is true? k l n m ∠k is an acute angle overline{kl} is congruent to overline{lm} overline{kl} is perpendicular to overline{nm} overline{kn} is congruent to overline{lm} 7 multiple choice 1 point which property is not common to all parallelograms? diagonals are congruent. opposite sides are parallel. consecutive angles are supplementary. opposite angles are congruent. 8 multiple choice 1 point a quadrilateral whose diagonals do not always bisect each other is a square an isosceles trapezoid a rhombus

Explanation:

Question 6

• For $\angle K$: In rectangle \(KLMN\), all angles are right angles (\(90^{\circ}\)). An acute angle is less than \(90^{\circ}\), so \(\angle K\) is not an acute angle.
• For \(\overline{KL}\) and \(\overline{LM}\): In a rectangle, adjacent sides (\(\overline{KL}\) and \(\overline{LM}\)) are not congruent (except in a square, but a rectangle is not necessarily a square).
• For \(\overline{KL}\) and \(\overline{NM}\): In a rectangle, \(\overline{KL}\parallel\overline{NM}\) (not perpendicular).
• For \(\overline{KN}\) and \(\overline{LM}\): In a rectangle, opposite sides are congruent. So \(\overline{KN}\cong\overline{LM}\) (by the property of rectangles: opposite sides of a rectangle are equal in length).

Question 7

• Opposite sides are parallel: This is a fundamental property of all parallelograms (by the definition of a parallelogram).
• Consecutive angles are supplementary: In a parallelogram, if \(\angle A\) and \(\angle B\) are consecutive angles, and \(AB\parallel CD\) with \(AD\) as a transversal, then \(\angle A+\angle B = 180^{\circ}\) (same - side interior angles).
• Opposite angles are congruent: Let \(\angle A\) and \(\angle C\) be opposite angles in parallelogram \(ABCD\). Using the properties of parallel lines (\(AB\parallel CD\) and \(AD\parallel BC\)) and transversals, we can prove \(\angle A\cong\angle C\).
• Diagonals are congruent: This is a property of rectangles (a special type of parallelogram), but not of all parallelograms. For example, in a non - rectangular parallelogram (a rhombus that is not a square), the diagonals are not congruent.

Question 8

• Square: The diagonals of a square bisect each other. In square \(ABCD\) with diagonals \(AC\) and \(BD\), \(AO = OC\) and \(BO=OD\) (where \(O\) is the intersection point of the diagonals).
• Isosceles trapezoid: The diagonals of an isosceles trapezoid are congruent, but they do not bisect each other. Let \(ABCD\) be an isosceles trapezoid with \(AD\parallel BC\) and \(AB = CD\). The diagonals \(AC\) and \(BD\) intersect at a point \(O\), but \(AO

eq OC\) and \(BO
eq OD\) in general.

• Rhombus: The diagonals of a rhombus bisect each other at right angles. In rhombus \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at \(O\), \(AO = OC\) and \(BO = OD\).

Answer:

1. \(\overline{KN}\) is congruent to \(\overline{LM}\)
2. Diagonals are congruent
3. an isosceles trapezoid