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Geometry, NAP-A3-CA19

Which one of these is a right-angled isosceles triangle?

NOT TO
 SCALE

 
 
 
 
 
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`text(Other angle)` `= 180 – (45 + 45)`
  `= 90^@`

 

`:.\ text(It is right-angled isosceles.)`

Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 7, smc-3165-15-Triangle properties, smc-679-15-Triangle properties

Geometry, NAP-A3-NC27

Tom drew this shape on grid paper.

Which one of the shapes below when joined to Tom's shape without an overlap, will not make isosceles triangle?

 
 
 
 

 

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Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 9, smc-3165-15-Triangle properties, smc-679-15-Triangle properties

Geometry, NAP-B3-CA28

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?

 
`b + c + d = 180^@`
 
`c + d + e = 360^@`
 
`a + b + f + g = 360^@`
 
`d + e + f + g = 180^@`
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`a + b + f + g = 360^@`

Show Worked Solution

`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^@`

Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 9, smc-3165-15-Triangle properties, smc-3165-25-Quadrilateral properties, smc-679-15-Triangle properties, smc-679-25-Quadrilateral properties

Geometry, NAP-G3-CA11

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)`

Show Worked Solution
`text(Base length)` `= 8 xx 0.7`
  `= 5.6\ text(metres)`

Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 7, smc-3165-15-Triangle properties, smc-679-15-Triangle properties

Geometry, NAP-I3-NC22

Which statement about the triangle pictured above is correct?

 
it is a right-angled triangle.
 
it is a scalene triangle.
 
it s an equilateral triangle.
 
it is an obtuse triangle.
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`text(it is an equilateral triangle.)`

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`text(The third angle of the triangle)\ = 180-(60+60) = 60°`

`:.\ text(It is an equilateral triangle.)`

Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 8, smc-3165-15-Triangle properties, smc-679-15-Triangle properties

Geometry, NAP-G4-NC18

`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)`

Show Worked Solution
`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.)`

Filed Under: Triangles and Other Geometric Properties, Triangles and Other Geometric Properties, Triangles and Other Geometric Properties Tagged With: Band 8, smc-3165-10-Triangles – find angle, smc-3165-15-Triangle properties, smc-3189-10-Triangles – find angle, smc-3189-35-Composite shapes, smc-680-10-Triangles - find angle, smc-680-35-Composite shapes

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