Question

3 fill in the blank 6 points
quadrilateral klmn is a parallelogram.
find lm
diagram of parallelogram klmn with kn labeled 5x + 1 and lm labeled 6x - 1
type your answer...
4 multiple choice 5 points
when proving that a quadrilateral is a parallelogram by using slopes, you must show that
2 pairs of sides have the same slope
all sides have different slopes
all sides have the same slope
2 pairs of sides have different slopes
5 multiple choice 6 points
which statement is true about every parallelogram?
the diagonals are perpendicular to each other.
two pairs of opposite sides are congruent.
all angles are congruent.
all four sides are congruent.

Explanation:

Question 3 (Fill in the Blank)

Step1: Recall Parallelogram Property

In a parallelogram, opposite sides are congruent. So, \( KN = LM \). Given \( KN = 5x + 1 \) and \( LM = 6x - 1 \), set them equal: \( 5x + 1 = 6x - 1 \).

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 1 = x - 1 \). Add 1 to both sides: \( x = 2 \).

Step3: Find \( LM \)

Substitute \( x = 2 \) into \( LM = 6x - 1 \): \( LM = 6(2) - 1 = 12 - 1 = 11 \).

A parallelogram has two pairs of parallel sides. Parallel lines have the same slope. So, to prove a quadrilateral is a parallelogram using slopes, we show 2 pairs of sides have the same slope. Other options are incorrect: "all sides different slopes" (no parallel sides), "all sides same slope" (implies all sides parallel, not a quadrilateral), "2 pairs different slopes" (no parallel sides).

• "Diagonals perpendicular": Only in rhombus/ square, not all parallelograms.
• "Two pairs opposite sides congruent": This is a defining property of parallelograms.
• "All angles congruent": Only in rectangles/ squares, not all parallelograms.
• "All four sides congruent": Only in rhombus/ square, not all parallelograms.

Answer:

11

Question 4 (Multiple Choice)