Podcast
Questions and Answers
Which type of parallelogram has diagonals that are congruent?
Which type of parallelogram has diagonals that are congruent?
- Square
- Trapezoid
- Rhombus
- Rectangle (correct)
What is the perimeter of parallelogram WXYZ if WZ = square root 26?
What is the perimeter of parallelogram WXYZ if WZ = square root 26?
2 square root 26 + 8 units
What are the two different angle measures of the parallelogram-shaped tile?
What are the two different angle measures of the parallelogram-shaped tile?
50° and 130°
What is the approximate sum of the lengths of the two sidewalks in a garden divided into sections?
What is the approximate sum of the lengths of the two sidewalks in a garden divided into sections?
What is the measure of angle MLP in rhombus LMNO if angle MLO measures 112°?
What is the measure of angle MLP in rhombus LMNO if angle MLO measures 112°?
What is the perimeter of parallelogram WXYZ if its sides are 2 square root 5 and 2 square root 17?
What is the perimeter of parallelogram WXYZ if its sides are 2 square root 5 and 2 square root 17?
What are the lengths of two adjacent sides of the parallelogram cut from construction paper?
What are the lengths of two adjacent sides of the parallelogram cut from construction paper?
Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
Which concept can be used to prove that the diagonals of a parallelogram bisect each other?
The midpoint of both diagonals in parallelogram HIJK is __________.
The midpoint of both diagonals in parallelogram HIJK is __________.
What is the missing reason in the proof that states BD ≅ AC in square ABCD?
What is the missing reason in the proof that states BD ≅ AC in square ABCD?
Which statement proves that PQRS is a parallelogram?
Which statement proves that PQRS is a parallelogram?
What is the perimeter of square ABCD?
What is the perimeter of square ABCD?
What is the value of p in parallelogram ABCD?
What is the value of p in parallelogram ABCD?
What is the perimeter of kite KLMN?
What is the perimeter of kite KLMN?
What is the length of line segment MX in parallelogram WXYZ?
What is the length of line segment MX in parallelogram WXYZ?
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Study Notes
Parallelograms
- Diagonals of a parallelogram are congruent in a rectangle.
- For parallelogram WXYZ, given WZ = √26, the perimeter is calculated as 2√26 + 8 units.
- Two opposite angles in a parallelogram-shaped tile measure (6n − 70)° and (2n + 10)°, resulting in angle measures of 50° and 130°.
Geometry Applications
- A garden measuring 15m by 23m has two sidewalks along the diagonals, with a total approximate length of 38.2 meters.
- In rhombus LMNO, if angle MLO measures 112°, then angle MLP measures 56°.
Side Lengths and Perimeters
- For parallelogram WXYZ, the perimeter can also be expressed as 2√5 + 2√17 units.
- Juanita finds two adjacent sides of her parallelogram to measure 4 cm and 7 cm, given dimensions (5n − 6) cm, (3n − 2) cm, and (2n + 3) cm.
Proving Properties
- The concept of congruent triangles can be applied to show that the diagonals of a parallelogram bisect each other.
- For parallelogram HIJK, the midpoint of both diagonals is located at (1, 0), confirming that the diagonals bisect each other.
Square Properties
- In square ABCD, to prove BD ≅ AC, the missing proof reason is "all sides of a square are congruent."
- The perimeter of square ABCD is calculated as 4√37.
Parallelogram Identification
- PQRS is identified as a parallelogram because both slopes of sides SP and RQ are -2, and SP = RQ = √45.
- In parallelogram WXYZ, sides are given as WY = 12 in., XZ = 16 in., WX = 10 in., and XY = 9 in.; length of segment MX is determined to be 8 in.
Kites
- The perimeter of kite KLMN is expressed as 2√2 + 2√5.
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