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Leaning Objectives
To learn about the properties of rectangles, rhombuses, and squares and to apply them while solving problems.

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Vocabulary

3. A rectangle is another special quadrilateral.
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A rectangle is another special quadrilateral.
A rectangle is a quadrilateral with four right angles.

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Since a rectangle is a parallelogram, a rectangle “inherits” all the properties of parallelograms.

5. A rectangular: JK = 50 cm and JL = 86 cm. Find HM.
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Example 1
A rectangular: JK = 50 cm and JL = 86 cm. Find HM.

6. The rectangular gate has diagonal braces. Find HJ.
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Example 2
The rectangular gate has diagonal braces. Find HJ.

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A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.
Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

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9. TVWX is a rhombus. Find TV.
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Example 3:
TVWX is a rhombus. Find TV.

10. TVWX is a rhombus. Find mVTZ.
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Example 4:
TVWX is a rhombus. Find mVTZ.

11. CDFG is a rhombus. Find CD.
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Example 5
CDFG is a rhombus. Find CD.

12. Example 6 CDFG is a rhombus. Find the measure.
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Example 6
CDFG is a rhombus.
Find the measure.
mGCH if mGCD = (b + 3)°
and mCDF = (6b – 40)°

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A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

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Rectangles, rhombuses, and squares are sometimes referred to as special parallelograms.
Helpful Hint

15. Example 7: Verifying Properties of Squares
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Example 7: Verifying Properties of Squares
Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

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Example 8
The vertices of square STVW are S(–5, –4), T(0, 2), V(6, –3) , and W(1, –9) . Show that the diagonals of square STVW are congruent perpendicular bisectors of each other.

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Example 9

18. In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length.
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Example 10
In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length.
1. TR CE

19. PQRS is a rhombus. Find each measure.
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Example 11
PQRS is a rhombus. Find each measure.
3. QP mQRP

20. Classify the special quadrilateral.
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Example 12
Classify the special quadrilateral.

21. Find the measures of the numbered angles in Rhombus DEFG.
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Example 13
Find the measures of the numbered
angles in Rhombus DEFG.

22. What is the m ADC and m BCD?
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Example 14
What is the m ADC and m BCD?

23. Find the measures of the numbered angles in rhombus ABCD.
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Example 15
Find the measures of the numbered angles in
rhombus ABCD.

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