Lesson 5 Rhombi and Squares
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Last updated 4 months ago
33 Nsɛmmisa
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Prove a Quadrilateral is a Rhombus
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Quadrilateral Family Tree
Using the applet on the previous slide, determine the properties of rhombus. Since a rhombus is a parallelogram, it will have all SIX parallelogram properties. A rhombus will also have an additional THREE "special" properties that distinguishes them from other parallelograms
Diagonals bisect its angles
Diagonals bisect each other
A diagonal divides the parallelogram into two congruent triangles
Only one pair of opposite sides congruent
Only one pair of opposite sides parallel
Both pairs of opposite sides are parallel
Diagonals are congruent.
Both pairs of opposite angles are congruent
4 congruent sides (Equilateral quadrilateral)
Both pairs of opposite sides are congruent
Consecutive angles are supplementary
Diagonals are perpendicular.
4 right angles (Equiangular quadrilateral)
QRST is a rhombus. Which of the following statements are (ALWAYS) TRUE?
m
True Statement
Not (necessarily) True
In rhombus QRST,
Explain your reasoning for your answer to the previous question.
In Rhombus QRST, which of the following statements MUST BE TRUE?
True Statement
When both diagonals of a rhombus are drawn, the diagonals form four rectangle into triangles.
List some right triangle applications, you might be able to apply when given a diagonal of a rhombus.
RSTV is a rhombus with diagonals
If
RSTV is a rhombus with diagonals
If m
m
RSTV is a rhombus with diagonals
If m
m
RSTV is a rhombus with diagonals
If m
and
RSTV is a rhombus with diagonals
Name three angles congruent to
RSTV is a rhombus with diagonals
Name three angles congruent to
RSTV is a rhombus with diagonals
Name three angles congruent to
RSTV is a rhombus with diagonals
Name three triangles congruent to
QRST is a rhombus with diagonals
If m
m
m
m
m
m
In Rhombus QRST,
Perimeter of QRST =
m
m
*Round answers to nearest tenth when necessary.
In Rhombus WXYZ,
Perimeter of WXYZ =
m
m
*Round answers to nearest tenth when necessary.
When using coordinate geometry to prove that a quadrilateral is a rhombus:
STEP 1 - Find the LENGTH (distance formula) of all 4 sides.
STEP 2 - Prove that quad is a parallelogram by showing that both pairs of opposite sides are congruent (2 sets of equal distances/lengths)
STEP 3 - Prove that parallelogram is a rhombus by showing that one pair of consecutive sides are congruent
Quadrilateral NATS has coordinates N(−4,−3), A(1,2), T(8,1), and S(3,−4). Prove quadrilateral NATS is a rhombus. [The use of the set of axes below is optional.]
Quadrilateral MATH has vertices M(−7,−2), A(0,4), T(9,2), and H(2,−4). Prove that parallelogram MATH is a rhombus. [The use of the set of axes below is optional.]
Quadrilateral MIKE has vertices with coordinates M(−1,−3), I(−3,3), K(5,4), and E(7,−2). Prove MIKE is a parallelogram, and prove MIKE is not a rhombus. [The use of the set of axes below is optional.]
Using the applet on the previous slide, determine the properties of square. Since a square is a parallelogram, it will have all SIX parallelogram properties. Since a square is a rectangle , it will have the TWO rectangle properties. Since a square is a rhombus, it will also have the THREE rhombus properties.
Both pairs of opposite sides are congruent
Both pairs of opposite sides are parallel
Diagonals are congruent.
Only one pair of opposite sides congruent
Both pairs of opposite angles are congruent
Diagonals are perpendicular.
A diagonal divides the parallelogram into two congruent triangles
4 right angles (Equiangular quadrilateral)
Diagonals bisect each other
Only one pair of opposite sides parallel
Diagonals bisect its angles
4 congruent sides (Equilateral quadrilateral)
Consecutive angles are supplementary
QRST is a square. Which of the following statements are (ALWAYS) TRUE?
m
True Statement
Not (necessarily) True
In Square QRST,
Explain your reasoning for your answer to the previous question.
In Square QRST, which of the following statements MUST BE TRUE?
True Statement
ABCD is a square.
If
ABCD is a square.
If
ABCD is a square.
Find:
m
m
m
m
m
ABCD is a square.
ABCD is a square. If
Perimeter of ABCD =
ABCD is a square. If
Perimeter of ABCD =
