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^@`
A ramp rises 1 metre for every 8 metres of its base length.
If it rises 0.7 metres, what is its base length?
`5.6\ text(metres)` | `8.7\ text(metres)` | `11.4\ text(metres)` | `16\ text(metres)` |
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`5.6\ text(metres)`
`text(Base length)` | `= 8 xx 0.7` |
`= 5.6\ text(metres)` |
Which statement about the triangle pictured above is correct?
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it is a right-angled triangle. |
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it is a scalene triangle. |
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it s an equilateral triangle. |
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it is an obtuse triangle. |
`text(it is an equilateral triangle.)`
`text(The third angle of the triangle)\ = 180-(60+60) = 60°`
`:.\ text(It is an equilateral triangle.)`
`AB` is the diameter of a circle, centre `O`.
There are 3 triangles drawn in the lower semi-circle and the angles at the centre are all equal to `x^@`.
The three triangles are best described as:
`text(isosceles)` | `text(scalene)` | `text(right-angled)` | `text(equilateral)` |
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`text(equilateral)`
`3x` | `=180` |
`:. x` | `=60^@` |
`AO=OC=OD=OB\ \ text{(radii of circle)}`
`=>\ text{Since angles opposite equal sides of a triangle are}`
`text(equal, all triangle angles can be found to equal 60°.)`
`:.\ text(The three triangles are equilateral.)`