smc-680-15-Triangle properties

Geometry, NAP-B4-NC21 SA

The area of the rectangle in the diagram below is 15 cm².

What is the area of the trapezium `ABCD`?

cm²

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`30\ text(cm)^2`

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`text{Opposite sides of rectangles are equal}`

`text(Triangles at bottom are congruent with the)`

`text{triangles the at top (RHS).}`

`text(Rearranging the diagram:)`

`:.\ text(Area of trapezium)`

`= 2 xx 15`

`= 30\ text(cm)^2`

Geometry, NAP-D4-NC22

Which one of the following triangles is impossible to draw?

	a right angled triangle with two acute angles
	an isosceles triangle with one right angle
	a scalene triangle with three acute angles
	a right angled triangle with one obtuse angle

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`text(a right angled triangle with one obtuse angle.)`

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`text(A right angle = 90°.)`

`text(S)text(ince an obtuse angle is greater than 90°, it)`

`text(is impossible for a triangle, with an angle sum)`

`text(less than 180°, to have both.)`

Geometry, NAP-E4-CA21

A triangle has two acute angles.

What type of angle couldn't the third angle be?

	an acute angle
	an obtuse angle
	a right-angle
	a reflex angle

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`text(reflex angle)`

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`text(A triangle’s angles add up to 180°, and a)`

`text(reflex angle is greater than 180°.)`

`:.\ text(The third angle cannot be reflex.)`

Geometry, NAP-F4-NC13

Which of the following triangle types is impossible to draw?

	a right-angled, isosceles triangle
	an acute-angled, isosceles triangle
	an obtuse-angled, scalene triangle
	a right-angled, equilateral triangle

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`text(a right-angled, equilateral triangle)`

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`text(An equilateral triangle has all angles = 60°.)`

`:.\ text(A right-angled, equilateral triangle is impossible.)`

Geometry, NAP-G4-NC23

`PQRSTU` are vertices on the cube below.

What is the best description of `DeltaPTR`?

isosceles	equilateral	right-angled	scalene

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`text(equilateral)`

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`PT, TR\ text(and)\ PR\ text(are all diagonals)`

`text(of the same sized square.)`

`:. PT = TR = PR`

`:. DeltaPTR\ text(is equilateral.)`

Geometry, NAP-G4-CA12

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)`

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

Geometry, NAP-I4-NC31 SA

Lee travels from `A` to `C` following the route `A -> B -> C` as shown in the diagram below.

How many metres less would Lee travel if he travelled directly from `A` to `C` as shown by the dotted line in the diagram?

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`text(200 m)`

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`text(Using Pythagoras,)`

`AC^2`	`= 300^2 + 400^2`
`:. AC^2`	`= 500^2`
`AC`	`= 500\ text(m)`

`A -> B -> C`

`= 300 + 400`

`= 700\ text(m)`

`:.\ text(Lee travels 200 m less.)`

Geometry, NAP-I4-NC19

Select the statement that is true about triangle `ABC`.

	Triangle `ABC` is a scalene triangle.
	Triangle `ABC` has exactly 2 equal sides.
	Triangle `ABC` is an equilateral triangle.
	Triangle `ABC` is an obtuse triangle.

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`text(Triangle)\ ABC\ text(is an equilateral.)`

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`angleA = 180-(60 + 60) = 60^@`

`:. text(All angles are)\ 60^@.`

`:. text(Triangle)\ ABC\ text(is an equilateral.)`

Geometry, NAP-I4-NC07

Vinny made a ramp to access his tree house that is 1.5 metres high.

The ratio of the horizontal length of the ramp to its height is `8:1`.

What is the horizontal length of the ramp?

`text(8 metres)`	`text(12 metres)`	`text(16 metres)`	`text(24 metres)`

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`text(12 metres)`

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`text(Ratio)`	`= 8:1`
	`= (8 xx 1.5):(1 xx 1.5)`
	`= 12:1.5`

`:.\ text(Horizontal length is 12 metres.)`