Podcast
Questions and Answers
In kite $KITE$, which statement about its diagonals is NOT always true?
In kite $KITE$, which statement about its diagonals is NOT always true?
- The diagonals are perpendicular.
- One diagonal bisects the other.
- The diagonal connecting the vertex angles bisects the other diagonal.
- The diagonals are congruent. (correct)
If the area of a kite is 36 square units and one of its diagonals is 12 units, what is the length of the other diagonal?
If the area of a kite is 36 square units and one of its diagonals is 12 units, what is the length of the other diagonal?
- 24 units
- 12 units
- 3 units
- 6 units (correct)
Which of the following statements is always true regarding the angles of a kite?
Which of the following statements is always true regarding the angles of a kite?
- All angles are equal.
- All angles are bisected by a diagonal.
- Opposite angles are supplementary.
- The vertex angles are bisected by a diagonal. (correct)
A quadrilateral is defined as a kite if:
A quadrilateral is defined as a kite if:
In kite $ABCD$, where $AB = AD$ and $CB = CD$, diagonal $AC$ intersects $BD$ at point $E$. If angle $BAC$ is 35 degrees, what is the measure of angle $DAE$?
In kite $ABCD$, where $AB = AD$ and $CB = CD$, diagonal $AC$ intersects $BD$ at point $E$. If angle $BAC$ is 35 degrees, what is the measure of angle $DAE$?
Which of the following statements accurately describes the defining characteristic of a trapezoid?
Which of the following statements accurately describes the defining characteristic of a trapezoid?
In trapezoid ABCD, where AB and CD are the bases, which line segment represents a leg of the trapezoid?
In trapezoid ABCD, where AB and CD are the bases, which line segment represents a leg of the trapezoid?
What distinguishes an isosceles trapezoid from a regular trapezoid?
What distinguishes an isosceles trapezoid from a regular trapezoid?
In $\triangle PQR$, points S and T are the midpoints of sides PQ and PR, respectively. If $QR = 12$, what is the length of the midsegment ST?
In $\triangle PQR$, points S and T are the midpoints of sides PQ and PR, respectively. If $QR = 12$, what is the length of the midsegment ST?
In trapezoid ABCD, M and N are the midpoints of legs AD and BC, respectively. If base $AB = 8$ and base $CD = 14$, what is the length of midsegment MN?
In trapezoid ABCD, M and N are the midpoints of legs AD and BC, respectively. If base $AB = 8$ and base $CD = 14$, what is the length of midsegment MN?
Which of the following is NOT a property of a parallelogram?
Which of the following is NOT a property of a parallelogram?
In isosceles trapezoid ABCD, where AB and CD are bases, which of the following statements must be true?
In isosceles trapezoid ABCD, where AB and CD are bases, which of the following statements must be true?
If the midsegment of a trapezoid has a length of 10, and one of the bases has a length of 8, what is the length of the other base?
If the midsegment of a trapezoid has a length of 10, and one of the bases has a length of 8, what is the length of the other base?
According to the Triangle Midsegment Theorem, what is the relationship between a triangle's midsegment and its third side?
According to the Triangle Midsegment Theorem, what is the relationship between a triangle's midsegment and its third side?
If a triangle's third side measures 10 cm, what is the length of its midsegment parallel to that side?
If a triangle's third side measures 10 cm, what is the length of its midsegment parallel to that side?
A trapezoid has bases of lengths 8 cm and 12 cm. According to the Trapezoid Midsegment Theorem, what is the length of its midsegment?
A trapezoid has bases of lengths 8 cm and 12 cm. According to the Trapezoid Midsegment Theorem, what is the length of its midsegment?
In trapezoid ABCD, where AB and CD are the bases, the midsegment EF is 9 cm. If AB is 6 cm, what is the length of CD?
In trapezoid ABCD, where AB and CD are the bases, the midsegment EF is 9 cm. If AB is 6 cm, what is the length of CD?
A roof is shaped like a trapezoid with the top horizontal line measuring 6 m and the base measuring 14 m. What is the length of the line that runs exactly in the middle of these two lines?
A roof is shaped like a trapezoid with the top horizontal line measuring 6 m and the base measuring 14 m. What is the length of the line that runs exactly in the middle of these two lines?
In $\triangle PQR$, points $X$ and $Y$ are the midpoints of sides $PQ$ and $PR$, respectively. If $XY = 7$ cm, what is the length of side $QR$?
In $\triangle PQR$, points $X$ and $Y$ are the midpoints of sides $PQ$ and $PR$, respectively. If $XY = 7$ cm, what is the length of side $QR$?
The upper base of a trapezoid is $x$ cm, and the lower base is $5x + 4$ cm. If the length of the median is 24 cm, find the length of the upper base.
The upper base of a trapezoid is $x$ cm, and the lower base is $5x + 4$ cm. If the length of the median is 24 cm, find the length of the upper base.
A gardener wants to divide a trapezoidal garden into two equal parts by building a fence along the midsegment. If the lengths of the parallel sides of the garden are 7 meters and 11 meters, how long should the fence be?
A gardener wants to divide a trapezoidal garden into two equal parts by building a fence along the midsegment. If the lengths of the parallel sides of the garden are 7 meters and 11 meters, how long should the fence be?
A trapezoid has bases of 7 meters and 13 meters and an area of 50 square meters. What is the height of the trapezoid?
A trapezoid has bases of 7 meters and 13 meters and an area of 50 square meters. What is the height of the trapezoid?
In isosceles trapezoid LOVE, LE and OV are parallel. If (\angle O) measures $98$ degrees, what is the measure of (\angle E)?
In isosceles trapezoid LOVE, LE and OV are parallel. If (\angle O) measures $98$ degrees, what is the measure of (\angle E)?
The median of a trapezoid is 9 cm. One base is twice the length of the other. What are the lengths of the bases?
The median of a trapezoid is 9 cm. One base is twice the length of the other. What are the lengths of the bases?
The diagonals of kite ABCD intersect at point E. If AC = 24 and BE = 5, what is the area of kite ABCD?
The diagonals of kite ABCD intersect at point E. If AC = 24 and BE = 5, what is the area of kite ABCD?
In kite WXYZ, (\angle WXY = 100^\circ). Which other angle must also measure (100^\circ)?
In kite WXYZ, (\angle WXY = 100^\circ). Which other angle must also measure (100^\circ)?
In kite ABCD, diagonal AC has a length of 10 cm, and diagonal BD has a length of 8 cm. What is the area of kite ABCD?
In kite ABCD, diagonal AC has a length of 10 cm, and diagonal BD has a length of 8 cm. What is the area of kite ABCD?
Kite PQRS has a perimeter of 66 cm. Sides PQ and PS are congruent, and sides QR and RS are congruent. If PQ is 15 cm, what is the length of QR?
Kite PQRS has a perimeter of 66 cm. Sides PQ and PS are congruent, and sides QR and RS are congruent. If PQ is 15 cm, what is the length of QR?
In quadrilateral RUBY (a kite), UY is double the length of UR, and the perimeter is 48 cm. Find the length of UY.
In quadrilateral RUBY (a kite), UY is double the length of UR, and the perimeter is 48 cm. Find the length of UY.
Flashcards
Triangle Midsegment
Triangle Midsegment
A line segment connecting the midpoints of two sides of a triangle.
Triangle Midsegment Theorem
Triangle Midsegment Theorem
A triangle's midsegment is half the length of the third side and parallel to it.
Midsegments and Congruence
Midsegments and Congruence
The three midsegments of a triangle divide it into four congruent triangles.
Trapezoid Midsegment
Trapezoid Midsegment
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Trapezoid Midsegment Theorem
Trapezoid Midsegment Theorem
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Midline of a triangle
Midline of a triangle
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Find the bases
Find the bases
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Word Problem
Word Problem
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Trapezoid
Trapezoid
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Bases of a Trapezoid
Bases of a Trapezoid
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Legs of a Trapezoid
Legs of a Trapezoid
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Isosceles Trapezoid
Isosceles Trapezoid
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Base Angles of a Trapezoid
Base Angles of a Trapezoid
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Midsegment (Midline) of a Trapezoid
Midsegment (Midline) of a Trapezoid
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Midsegment (Midline) of a Triangle
Midsegment (Midline) of a Triangle
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Definition of the midsegment of a trapezoid
Definition of the midsegment of a trapezoid
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What is a Kite?
What is a Kite?
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Kite Diagonals Theorem
Kite Diagonals Theorem
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Kite Diagonal Bisector Theorem
Kite Diagonal Bisector Theorem
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Kite Angle Bisector Theorem
Kite Angle Bisector Theorem
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What is a trapezoid?
What is a trapezoid?
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Area of a Trapezoid Formula
Area of a Trapezoid Formula
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Median of a Trapezoid
Median of a Trapezoid
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Median of a Trapezoid Formula
Median of a Trapezoid Formula
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Kite
Kite
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Area of a Kite
Area of a Kite
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Kite Diagonals
Kite Diagonals
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Kite Angles Theorem
Kite Angles Theorem
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Study Notes
- Trapezoids and kites are quadrilaterals, but not parallelograms.
- The goal is to be able to apply the Midline Theorem, prove theorems, and solve problems involving triangles.
- A recall on statements about quadrilaterals, parallelograms, rectangles, and squares needs to be considered.
trapezoids and isosceles trapezoids
- A trapezoid is a quadrilateral containing only one set of parallel sides.
- The parallel sides are its bases, and the nonparallel sides are its legs.
- An isosceles trapezoid is a trapezoid whose legs are of equal length.
Midline Theorem
- Connecting the midpoints of two sides of a triangle creates its midsegment or midline.
- In a trapezoid, the midsegment links the midpoints of the nonparallel sides.
- The Midline Theorem states that a triangle's midsegment will be half the lentgh of the third side, and it will be parallel to it.
Proving theorems
- The midsegments divide a triangle into four congruent triangles.
- One can apply the Side-Angle-Side (SAS) Postulate to prove congruence.
- The segment between the midpoints of two triangle sides is parallel to the third side and half its length.
- A trapezoid midsegment is parallel to its bases.
Examples
- Applying the triangle midsegment theorem, and being able to sub answers correctly in formulas.
- Applying the trapezoid midsegment theorem, and being able to sub answers correctly in formulas.
- Length of Trapezoid Median: 18 cm, Lower base +16 cm longer than the lengths of the upper base
- Flower garden shaped like trapezoid with base 4m & 5m & fence in the middle
Word Problems
- The area of a trapezoid is calculated by 1/2 * height * (base1 + base2).
- Quadrilateral LOVE is an isosceles trapezoid, where sides LE & OV are parallel and sides LO & EV are equal. UR is the median.
- Vertex angles in a trapezoid are supplementary, meaning that their measures will add up to 180°.
Kite Theorems
- A kite area is calculated as one-half the product of its diagonal lengths.
- Kite diagonals intersect at a 90-degree angle and one diagonal bisects the other.
- A kite is a quadrilateral that contains unique pairs of corresponding and conjoining sides.
- Non-vertex kite angles are congruent.
- The vertex angles in a kite are bisected by the kites diagonal
Kite Theorems:
- Diagonals are perpendicular.
- The diagonal that touches the vertex angles bisects the other ones.
- The vertex angles in a kite get bisected by its own diagonal
Seatwork practice
- State if the following are true/false:
- Isosceles trapezoids have congruent diagonals.
- Parallel sides of an isosceles trapezoid are the same length.
- Opposite angles in a kite can add up to 180 degrees.
- The line connecting the midpoints of the non-parallel sides of a trapezoid is called the mean.
- The area of a kite is calculated by taking twice the product of its diagonal lengths.
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Description
Review of trapezoids, kites, and the Midline Theorem. This includes applying the Midline Theorem and proving theorems involving triangles. Recall statements about quadrilaterals, parallelograms, rectangles, and squares.
