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Questions and Answers
In quadrilateral $ABCD$, $\angle A = 50^\circ$ and $\angle B = 130^\circ$. What additional information is sufficient to prove that $ABCD$ is a parallelogram?
In quadrilateral $ABCD$, $\angle A = 50^\circ$ and $\angle B = 130^\circ$. What additional information is sufficient to prove that $ABCD$ is a parallelogram?
- $\angle C = 50^\circ$ (correct)
- $AD \cong BC$
- $\angle C = 120^\circ$
- $AB \cong CD$
A quadrilateral has diagonals that are perpendicular but not congruent. Which of the following is the most precise classification of this quadrilateral?
A quadrilateral has diagonals that are perpendicular but not congruent. Which of the following is the most precise classification of this quadrilateral?
- Rhombus (correct)
- Parallelogram
- Square
- Rectangle
In parallelogram $EFGH$, $EG = x + 15$ and $FH = 3x - 5$. What value of $x$ would prove that $EFGH$ is a rectangle?
In parallelogram $EFGH$, $EG = x + 15$ and $FH = 3x - 5$. What value of $x$ would prove that $EFGH$ is a rectangle?
- 20
- 15
- 5
- 10 (correct)
Which statement is sufficient to prove that a quadrilateral is a square?
Which statement is sufficient to prove that a quadrilateral is a square?
The midsegment of a trapezoid measures 18 cm. If one of the bases is 10 cm, what is the length of the other base?
The midsegment of a trapezoid measures 18 cm. If one of the bases is 10 cm, what is the length of the other base?
In rhombus $ABCD$, $\angle BAC = 32^\circ$. What is the measure of $\angle BCD$?
In rhombus $ABCD$, $\angle BAC = 32^\circ$. What is the measure of $\angle BCD$?
Which of the following statements is NOT always true for a parallelogram?
Which of the following statements is NOT always true for a parallelogram?
In isosceles trapezoid $PQRS$, $PQ \parallel RS$. If $\angle P = 70^\circ$, what is the measure of $\angle R$?
In isosceles trapezoid $PQRS$, $PQ \parallel RS$. If $\angle P = 70^\circ$, what is the measure of $\angle R$?
Flashcards
Quadrilateral
Quadrilateral
A polygon with four sides.
Parallelogram
Parallelogram
A quadrilateral with both pairs of opposite sides parallel.
Parallelogram Property
Parallelogram Property
Opposite sides are congruent.
Rectangle
Rectangle
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Rhombus
Rhombus
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Square
Square
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Trapezoid
Trapezoid
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Isosceles Trapezoid
Isosceles Trapezoid
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Study Notes
- A quadrilateral is a polygon with four sides
- The sum of the interior angles of a quadrilateral is 360 degrees
Parallelograms
- A parallelogram is a quadrilateral with both pairs of opposite sides parallel
- Parallelograms have specific properties
- Opposite sides are congruent
- Opposite angles are congruent
- Consecutive angles are supplementary, totaling 180 degrees
- Diagonals bisect each other
- A quadrilateral is a parallelogram if any of these are true
- Both pairs of opposite sides are parallel
- Both pairs of opposite sides are congruent
- Both pairs of opposite angles are congruent
- One pair of opposite sides is both parallel and congruent
- The diagonals bisect each other
Rectangles
- A rectangle is a parallelogram with four right angles
- Properties of rectangles include
- All properties of a parallelogram
- All four angles are right angles
- Diagonals are congruent
- A parallelogram is a rectangle when
- It has four right angles
- Its diagonals are congruent
Rhombi
- A rhombus (plural: rhombi) is a parallelogram with four congruent sides
- Properties of rhombi include
- All properties of a parallelogram
- All four sides are congruent
- Diagonals are perpendicular
- Diagonals bisect the angles of the rhombus
- A parallelogram is a rhombus when
- It has four congruent sides
- Its diagonals are perpendicular
Squares
- A square is a parallelogram with four congruent sides and four right angles
- A square is both a rectangle and a rhombus
- Properties of squares include
- All properties of parallelograms, rectangles, and rhombi
- All four sides are congruent
- All four angles are right angles
- Diagonals are congruent
- Diagonals are perpendicular
- Diagonals bisect the angles of the square and create two 45-degree angles
Trapezoids
- A trapezoid is a quadrilateral with exactly one pair of parallel sides
- Bases are the parallel sides
- Legs are the non-parallel sides
- Base angles are formed by a base and a leg
- An isosceles trapezoid is a trapezoid with congruent legs
- Properties of isosceles trapezoids include
- Base angles are congruent
- Diagonals are congruent
- A trapezoid is isosceles when
- It has congruent base angles
- It has congruent diagonals
- The midsegment of a trapezoid connects the midpoints of the legs
- The midsegment is parallel to the bases
- The length of the midsegment is the average of the lengths of the bases
Kites
- A kite is a quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent
- Properties of kites include
- Diagonals are perpendicular
- Exactly one pair of opposite angles is congruent
- The diagonal connecting the congruent angles bisects the other diagonal
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Description
Learn about quadrilaterals, polygons with four sides, and parallelograms with opposite sides parallel. Explore properties like congruent sides/angles and supplementary angles. Discover how to prove a quadrilateral is a parallelogram.
