Podcast
Questions and Answers
Given parallelogram HOME, which additional piece of information would be sufficient to prove that HOME is a rhombus?
Given parallelogram HOME, which additional piece of information would be sufficient to prove that HOME is a rhombus?
- Diagonal OE is perpendicular to diagonal HM. (correct)
- Diagonal HE is congruent to diagonal OM.
- Angle HOM is congruent to angle HME.
- HOME has four right angles.
In rhombus PLAN, if $m\angle PLA = 60$, then $m\angle PAN = 60$ degrees.
In rhombus PLAN, if $m\angle PLA = 60$, then $m\angle PAN = 60$ degrees.
False (B)
In rhombus ABCD, $m\angle ABE = (4x - 15)$° and $m\angle CBE = (x + 21)$°. Find $m\angle ABE$.
In rhombus ABCD, $m\angle ABE = (4x - 15)$° and $m\angle CBE = (x + 21)$°. Find $m\angle ABE$.
63
In rectangle WXYZ, if XZ = 2x - 9 and YW = x + 12, then YW = _______.
In rectangle WXYZ, if XZ = 2x - 9 and YW = x + 12, then YW = _______.
Match the properties with the corresponding quadrilaterals.
Match the properties with the corresponding quadrilaterals.
Which property is unique to rectangles compared to all other parallelograms?
Which property is unique to rectangles compared to all other parallelograms?
All squares are rhombuses, but not all rhombuses are squares.
All squares are rhombuses, but not all rhombuses are squares.
A parallelogram has diagonals that are perpendicular and bisect each other. What specific type of parallelogram is it?
A parallelogram has diagonals that are perpendicular and bisect each other. What specific type of parallelogram is it?
If the diagonals of a parallelogram are congruent, then the parallelogram is a ______.
If the diagonals of a parallelogram are congruent, then the parallelogram is a ______.
Match the parallelogram with the property of its diagonals:
Match the parallelogram with the property of its diagonals:
In parallelogram ABCD, diagonals AC and BD intersect at point E. If AE = 3x + 2 and EC = 5x - 8, what is the length of AC if ABCD is a rectangle?
In parallelogram ABCD, diagonals AC and BD intersect at point E. If AE = 3x + 2 and EC = 5x - 8, what is the length of AC if ABCD is a rectangle?
A parallelogram with one right angle must be a rectangle.
A parallelogram with one right angle must be a rectangle.
Which of the following conditions would guarantee that a parallelogram is a rhombus?
Which of the following conditions would guarantee that a parallelogram is a rhombus?
Flashcards
Rhombus
Rhombus
A parallelogram with four congruent sides.
Rectangle
Rectangle
A parallelogram with four right angles.
Square
Square
A parallelogram with four congruent sides and four right angles.
Rhombus Angle Property
Rhombus Angle Property
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Rectangle Diagonal Property
Rectangle Diagonal Property
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Rectangle Diagonals
Rectangle Diagonals
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Rhombus Diagonals
Rhombus Diagonals
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Rhombus Diagonal Angle Bisectors
Rhombus Diagonal Angle Bisectors
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Congruent Diagonals
Congruent Diagonals
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Perpendicular Diagonals
Perpendicular Diagonals
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Study Notes
- Rectangles, rhombuses, and squares are geometric shapes.
- Gabrielle J. Soriano, LPT created this presentation.
- The goal is to learn about geometric shapes as special parallelograms.
- Theorems on the kinds of parallelograms will be identified. Solve problems involving the different kinds of parallelograms.
Special Parallelograms
- Rectangles, rhombuses and squares are special parallelograms.
- Properties of a parallelogram hold true for each geometric shape.
Definitions
- A rectangle is a parallelogram with four right angles.
- A rhombus is a parallelogram with four congruent sides.
- A square is a parallelogram with four right angles and four congruent sides.
Theorem 5.2a: Diagonals of a Rectangle
- If a parallelogram is a rectangle, then its diagonals are congruent.
Theorem 5.2b: Diagonals of a Rhombus
- If a parallelogram is a rhombus, then its diagonals are perpendicular.
Theorem 5.2c
- If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.
Theorem 5.2d
- If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 5.2e
- If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 5.2f
- If the diagonals of a parallelogram bisect both pairs of opposite angles, then the parallelogram is a rhombus.
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