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Questions and Answers
In a trapezoid with bases of length 10 cm and 18 cm, what is the length of the midsegment?
In a trapezoid with bases of length 10 cm and 18 cm, what is the length of the midsegment?
- 16 cm
- 14 cm (correct)
- 18 cm
- 12 cm
In triangle ABC, M is the midpoint of AB and N is the midpoint of AC. If MN = 5 cm, what is the length of BC?
In triangle ABC, M is the midpoint of AB and N is the midpoint of AC. If MN = 5 cm, what is the length of BC?
- 15 cm
- 10 cm (correct)
- 5 cm
- 20 cm
The midsegment of a trapezoid is parallel to the bases and equal to half the sum of the bases. If the bases of a trapezoid are 8 cm and 12 cm, what is the length of the midsegment?
The midsegment of a trapezoid is parallel to the bases and equal to half the sum of the bases. If the bases of a trapezoid are 8 cm and 12 cm, what is the length of the midsegment?
- 8 cm
- 10 cm (correct)
- 16 cm
- 12 cm
A trapezoid has a midsegment of length 10 cm. One of its bases is 6 cm long. What is the length of the other base?
A trapezoid has a midsegment of length 10 cm. One of its bases is 6 cm long. What is the length of the other base?
In triangle XYZ, P is the midpoint of XY and Q is the midpoint of XZ. If PQ = 7 cm, what is the length of YZ?
In triangle XYZ, P is the midpoint of XY and Q is the midpoint of XZ. If PQ = 7 cm, what is the length of YZ?
In a trapezoid, the midsegment is 10 cm long, and one base is 12 cm longer than the other. What is the length of the shorter base?
In a trapezoid, the midsegment is 10 cm long, and one base is 12 cm longer than the other. What is the length of the shorter base?
If the length of the midsegment of a trapezoid is 15 cm and the length of one base is 20 cm, what is the length of the other base?
If the length of the midsegment of a trapezoid is 15 cm and the length of one base is 20 cm, what is the length of the other base?
In a triangle, the midsegment is 8 cm long. What is the length of the side of the triangle that is parallel to the midsegment?
In a triangle, the midsegment is 8 cm long. What is the length of the side of the triangle that is parallel to the midsegment?
In trapezoid ABCD, where AB || CD, if AB = 10 cm, CD = 18 cm, and EF is the midsegment, what is the length of EF?
In trapezoid ABCD, where AB || CD, if AB = 10 cm, CD = 18 cm, and EF is the midsegment, what is the length of EF?
If a trapezoid has a midsegment of 9 cm and a base of 12 cm, what is the length of the other base?
If a trapezoid has a midsegment of 9 cm and a base of 12 cm, what is the length of the other base?
If the length of one base of an isosceles trapezoid is double the length of the other base, and the median (UR) measures 6 centimeters, what is the length of each leg?
If the length of one base of an isosceles trapezoid is double the length of the other base, and the median (UR) measures 6 centimeters, what is the length of each leg?
In quadrilateral LOVE, LE = 3x – 7cm, OV = 2x + 1cm and UR = 12cm. What is the value of x?
In quadrilateral LOVE, LE = 3x – 7cm, OV = 2x + 1cm and UR = 12cm. What is the value of x?
In quadrilateral LOVE, LE = 3x – 7cm, OV = 2x + 1cm and UR = 12cm. What is the length of LE?
In quadrilateral LOVE, LE = 3x – 7cm, OV = 2x + 1cm and UR = 12cm. What is the length of LE?
In quadrilateral LOVE, if the measure of angle O is 2x – 9 and the measure of angle L is 2x + 5, what is the measure of angle E?
In quadrilateral LOVE, if the measure of angle O is 2x – 9 and the measure of angle L is 2x + 5, what is the measure of angle E?
If the length of UY is double the length of UR, and the perimeter of kite RUBY is 42 centimeters, what is the length of UY?
If the length of UY is double the length of UR, and the perimeter of kite RUBY is 42 centimeters, what is the length of UY?
What is the area of kite RUBY if RY = 15 cm and UB = 8 cm?
What is the area of kite RUBY if RY = 15 cm and UB = 8 cm?
If the length of one base of a trapezoid is 10 cm and the length of the median is 14 cm, what is the length of the other base?
If the length of one base of a trapezoid is 10 cm and the length of the median is 14 cm, what is the length of the other base?
Given the area of a trapezoid is 80 m^2, the height of the trapezoid is 8 m, and one base is 5 m, what is the length of the other base?
Given the area of a trapezoid is 80 m^2, the height of the trapezoid is 8 m, and one base is 5 m, what is the length of the other base?
In quadrilateral LOVE, if LE = 10 cm, OV = 15 cm, and UR = 12.5 cm, what is the length of the median?
In quadrilateral LOVE, if LE = 10 cm, OV = 15 cm, and UR = 12.5 cm, what is the length of the median?
In a trapezoid, if the midsegment is 10 units long and one base is 6 units, what is the length of the other base?
In a trapezoid, if the midsegment is 10 units long and one base is 6 units, what is the length of the other base?
If the diagonals of a trapezoid are congruent, what type of trapezoid is it?
If the diagonals of a trapezoid are congruent, what type of trapezoid is it?
In a trapezoid ABCD, with AB parallel to CD, if AB = 8 cm and CD = 12 cm, what is the length of the midsegment?
In a trapezoid ABCD, with AB parallel to CD, if AB = 8 cm and CD = 12 cm, what is the length of the midsegment?
If one angle of a trapezoid is 100 degrees, what is the measure of its consecutive angle?
If one angle of a trapezoid is 100 degrees, what is the measure of its consecutive angle?
A trapezoid has two right angles. What type of trapezoid is it?
A trapezoid has two right angles. What type of trapezoid is it?
In a trapezoid ABCD, with AB parallel to CD, if AB is twice the length of CD, what is the ratio of the area of triangle ABD to the area of triangle BCD?
In a trapezoid ABCD, with AB parallel to CD, if AB is twice the length of CD, what is the ratio of the area of triangle ABD to the area of triangle BCD?
If the midsegment of a trapezoid is 5 cm long and one base is 3 cm long, what is the length of the other base?
If the midsegment of a trapezoid is 5 cm long and one base is 3 cm long, what is the length of the other base?
Which of the following statements is true about the diagonals of an isosceles trapezoid?
Which of the following statements is true about the diagonals of an isosceles trapezoid?
In a trapezoid, the non-parallel sides are called:
In a trapezoid, the non-parallel sides are called:
If the area of a trapezoid is 30 square units and the height is 5 units, what is the sum of the lengths of the two bases?
If the area of a trapezoid is 30 square units and the height is 5 units, what is the sum of the lengths of the two bases?
Which of the following theorems is directly related to the property that the diagonals of a kite are perpendicular?
Which of the following theorems is directly related to the property that the diagonals of a kite are perpendicular?
Which of the following statements about kites is FALSE?
Which of the following statements about kites is FALSE?
Which statement regarding isosceles trapezoids is TRUE?
Which statement regarding isosceles trapezoids is TRUE?
A kite differs from a rhombus in which of the following aspects?
A kite differs from a rhombus in which of the following aspects?
Which property is shared by both kites and isosceles trapezoids?
Which property is shared by both kites and isosceles trapezoids?
The area of a kite is determined by:
The area of a kite is determined by:
If the lengths of the two diagonals of a kite are 6 cm and 8 cm respectively, what is the area of the kite?
If the lengths of the two diagonals of a kite are 6 cm and 8 cm respectively, what is the area of the kite?
What statement is TRUE about the line connecting the midpoints of the non-parallel sides of a trapezoid?
What statement is TRUE about the line connecting the midpoints of the non-parallel sides of a trapezoid?
A trapezium with exactly two parallel sides is specifically called a:
A trapezium with exactly two parallel sides is specifically called a:
Given a kite with one pair of adjacent sides measuring 5 cm and another pair measuring 7 cm, what is the perimeter of the kite?
Given a kite with one pair of adjacent sides measuring 5 cm and another pair measuring 7 cm, what is the perimeter of the kite?
Flashcards
Kite Diagonals Theorem
Kite Diagonals Theorem
The diagonals of a kite are perpendicular to each other.
Kite Diagonal Bisector Theorem
Kite Diagonal Bisector Theorem
The diagonal connecting the vertex angles is the perpendicular bisector of the other diagonal.
Kite Angle Bisector Theorem
Kite Angle Bisector Theorem
The vertex angles of a kite are bisected by its diagonal.
Isosceles Trapezoid
Isosceles Trapezoid
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Congruent Diagonals
Congruent Diagonals
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Opposite Angles in a Kite
Opposite Angles in a Kite
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Mean of a Trapezoid
Mean of a Trapezoid
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Area of a Kite
Area of a Kite
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Perpendicular Lines
Perpendicular Lines
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Quadrilateral
Quadrilateral
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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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Midsegment of a triangle
Midsegment of a triangle
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Midsegment of a trapezoid
Midsegment of a trapezoid
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Kite (in geometry)
Kite (in geometry)
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Midline Theorem
Midline Theorem
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Properties of parallelograms
Properties of parallelograms
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Area of a Trapezoid
Area of a Trapezoid
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Kite
Kite
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Kite Area Formula
Kite Area Formula
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Kite Diagonal Intersection
Kite Diagonal Intersection
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Congruent Angles in a Kite
Congruent Angles in a Kite
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Perimeter of a Kite
Perimeter of a Kite
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Angle Measures in Isosceles Trapezoid
Angle Measures in Isosceles Trapezoid
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Finding Base Lengths
Finding Base Lengths
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Triangle Midsegment Theorem
Triangle Midsegment Theorem
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Congruent triangles
Congruent triangles
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Trapezoid Midsegment
Trapezoid Midsegment
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Length of a midsegment
Length of a midsegment
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Base of Trapezoid
Base of Trapezoid
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Finding upper base
Finding upper base
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Application of the midsegment theorem
Application of the midsegment theorem
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Study Notes
Trapezoids and Kites
- Trapezoids and kites are quadrilaterals that are not parallelograms.
- A trapezoid is a quadrilateral with exactly one pair of parallel sides.
- The parallel sides of a trapezoid are called bases.
- The non-parallel sides of a trapezoid are called legs.
- Base angles are angles formed by the base and a leg.
- Specific types of trapezoids include isosceles trapezoids which have legs of equal length. The base angles of equal measure.
Learning Objectives
- Students will apply the Midline Theorem to solve problems involving triangles.
- Students will prove theorems of trapezoids and kites.
- Students will solve problems involving parallelograms, trapezoids, and kites.
Review of Quadrilaterals
- All quadrilaterals have four sides.
- Squares are a specific type of rectangle.
- Parallelograms have two sets of parallel sides.
- Rectangles have four right angles.
- Squares have four equal sides.
- Opposite sides of a parallelogram are equal in length.
- Consecutive angles in a parallelogram have a sum of 180 degrees.
- The diagonals of a parallelogram intersect at their midpoints.
- A diagonal divides a parallelogram into two identical triangles.
Trapezoid Midsegment Theorem
- A trapezoid's midsegment is parallel to its bases and has a length equal to half the sum of the lengths of its bases.
- e.g., EF = 1/2 (BC + AD)
Triangle Midsegment Theorem
- A triangle's midsegment is parallel to the third side and is half its length.
- e.g., TU = 1/2 (NV)
Kite Properties
- A kite's diagonals are perpendicular.
- One diagonal of a kite bisects the other.
- The non-vertex angles of a kite are congruent.
Kite Area
- The area of a kite is one-half the product of the lengths of its diagonals.
Example Problems
- Example problems demonstrate how to calculate the lengths of midsegments and bases, and apply the theorems. These involve identifying congruent parts, finding missing values, and solving for unknown variables. The use of equations and geometric principles are shown.
- The length of one base of the trapezoid is double the length of the other base.
- Example problems to solve find unknown values/lengths, and find area given values.
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