1. 9.3 Rectangles, Rhombuses and Squares
Additional Example 4
Additional Example 5
Additional Example 6
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2. Additional Example 4
In the figure, ABCD is a rectangle. Find a, b, c and d.
Solution
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3. Solution AO = OD (property of rectangle)
Additional Example 4
In the figure, ABCD is a rectangle. Find a, b, c and d.
Solution
AO = OD
(property of rectangle)
 AOD is an isosceles triangle.
OAD = b
(base s, isos. )
OAD + ADO + AOD = 180
( sum of )
b + b + 60 = 180
2b = 120
b = 60
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4. Solution AOB + 60 = 180 (adj. s on st. line) AOB = 120 AO = OB
Additional Example 4
In the figure, ABCD is a rectangle. Find a, b, c and d.
Solution
AOB + 60 = 180
(adj. s on st. line)
AOB = 120
AO = OB
(property of rectangle)
 AOB is an isosceles triangle.
BAO = 3a
(base s, isos. )
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5. Solution OAB + ABO + AOB = 180 ( sum of ) 3a + 3a + 120 = 180
Additional Example 4
In the figure, ABCD is a rectangle. Find a, b, c and d.
Solution
OAB + ABO + AOB = 180
( sum of )
3a + 3a + 120 = 180
6a = 60
a = 10
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6. Solution AO = OC (property of rectangle) c – 2 = 10 c = 12 OB = OC
Additional Example 4
In the figure, ABCD is a rectangle. Find a, b, c and d.
Solution
AO = OC
(property of rectangle)
c – 2 = 10
c = 12
OB = OC
(property of rectangle)
d – 6 = 10
d = 16
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7. Additional Example 5 In the figure, ABCD is a square. Find a, b and c.
Solution
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8. Solution (property of square) a = 45 3b = 90 (property of square)
Additional Example 5
In the figure, ABCD is a square. Find a, b and c.
Solution
(property of square)
a = 45
3b = 90
(property of square)
b = 30
CD = AD =　　 cm
(property of square)
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9. Solution ADC = 90 (property of square)  AC2 = AD2 + CD2
Additional Example 5
In the figure, ABCD is a square. Find a, b and c.
Solution
ADC = 90
(property of square)
 AC2 = AD2 + CD2
(Pyth. Theorem)
= 100
= 10 cm
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10. Solution (property of square)  OC = 5 cm 3c + 2 = 5 3c = 3 c = 1
Additional Example 5
In the figure, ABCD is a square. Find a, b and c.
Solution
 OC
(property of square)
= 5 cm
3c + 2 = 5
3c = 3
c = 1
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11. Additional Example 6
ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z.
Solution
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12. Solution DBC = ABD = 28 (property of rhombus) ADC = ABC
Additional Example 6
ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z.
Solution
DBC = ABD = 28
(property of rhombus)
ADC = ABC
(property of rhombus)
x = ABD + DBC
= 28 + 28
= 56
BDC =　　
= 28
(property of rhombus)
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13. Solution In DBC, BDC + DCB + CBD = 180 ( sum of )
Additional Example 6
ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z.
Solution
In DBC,
BDC + DCB + CBD = 180
( sum of )
28 + 28 + y = 180
y = 124
DFE = w
(vert. opp. s)
In FDE,
FDE + DFE = AEC
(ext.  of )
28 + w = 90
w = 62
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14. Solution In ADE, DAE + ADE = 90 (ext.  of ) z + x = 90
Additional Example 6
ABCD is a rhombus with ABD = 28 and AE  DC. Find w, x, y and z.
Solution
In ADE,
DAE + ADE = 90
(ext.  of )
z + x = 90
z = 90 – x
= 90 – 56
= 34
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