Question
Question 3 (1 point)
(04.01 MC)
Figure LMNO is located at
a Kite
b Parallelogram
c Square
đ Trapezoid
(04.01 MC)
a Kite
b Parallelogram
c Square
đ Trapezoid
Ask by Tyler Bartlett. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Quadrilateral LMNO is a square.
Solution
To classify quadrilateral LMNO with vertices
-
Calculate Side Lengths:
- LM:
- MN:
- NO:
- OL:
All sides are equal in length, suggesting a rhombus or square. - LM:
-
Calculate Slopes:
- Slope LM:
- Slope MN:
- Slope NO:
- Slope OL:
Adjacent sides have slopes that are negative reciprocals, indicating perpendicularity. Hence, all angles are right angles. - Slope LM:
-
Check Diagonals:
- Diagonal LN: Length
and slope (horizontal). - Diagonal MO: Length
and undefined slope (vertical).
The diagonals are equal in length and perpendicular, confirming that the quadrilateral is a square. - Diagonal LN: Length
Answer:
c Square
c Square
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To classify quadrilateral LMNO, we first calculate the lengths of its sides and examine its diagonals. The lengths of the sides provide information about parallelism and equality, which are key traits for classification. By finding the distances between each pair of points, we can determine that sides LM and ON are equal, as are the lengths of LO and MN, indicating a special shape.
Additionally, checking if the diagonals intersect at their midpoints can further reveal if this quadrilateral is a parallelogram. However, because one pair of opposite sides is equal and not parallel, the best classification for quadrilateral LMNO is a kite, as it has two pairs of adjacent sides that are equal in length without opposing sides being congruent.
The classification of quadrilaterals can also be determined by the characteristics of their angles. For instance, a kite has congruent angles between unequal pairs of sides, which adds to its distinct form. While a parallelogram features opposite sides that are equal and parallel, knowing these criteria helps you navigate through geometry with confidence!
