Aussie Maths & Science Teachers: Save your time with SmarterEd
A triangle is divided into 2 parts by a straight line.
The angles are then labelled.
Which statement is true about the sum of angles?
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`b + c + d = 180^@` |
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`c + d + e = 360^@` |
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`a + b + f + g = 360^@` |
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`d + e + f + g = 180^@` |
`a + b + f + g = 360^@`
`text(Consider each option:)`
`text(Option 1:)\ \ b + c + d != 180`
`=> b+c = 180^@`
`text(Option 2:)\ \ c + d + e != 360^@`
`=> c + d + e = 180^@\ \ text{(angle sum of triangle)}`
`text(Option 3:)\ \ a + b + f + g = 360^@`
`=>\ text(Correct since the angle sum of a quadrilateral = 360°)`
`text(Option 4:)\ \ d + e + f + g != 180`
`=> e + f = 180^@`
Murphy draws and labels 3 points, on a Cartesian plane.
He wants to add another point so that all 4 points can be joined to make a parallelogram.
Which of these is a possible coordinate for the 4th point?
`(−1,2)` | `(1,5)` | `(2,−1)` | `(5,1)` |
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`( – 1, 2)`
`text(One Strategy:)`
`text{Consider the point (4, 4). The point below is 2 units down and)`
`text{2 units left. Apply this to the point (1, 4).}`
`:. ( – 1, 2)\ \ text(is the vertex of a parallelogram.)`
`text{Note that (5, 2) will also make a parallelogram but this point is}`
`text(is not given as an option.)`