22477529
Description
Mind Map by Rhianna Sangha, updated more than 1 year ago
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Created by Rhianna Sangha
over 4 years ago
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Constructing Triangles and Loci
- 3 properties that are
needed to construct a
triangle
- SAS-Side, Angle, Side
- SSS-All three sides
- ASA-Angle, Side, Angle
- SAS-Side, Angle, Side
- Constructing Triangles Worked Examples
- SAS
- Draw a triangle with sides of 4cm and 6cm and an angle of 40°.
- 1) Draw the longest side
using a ruler
- 2) Label the ends A and B
- 3) Measure a 40° angle from point A
and draw a 4cm line
- 4) Label this line C
- 5)Draw a line from point B
to point C
- There you have
a finished
triangle
- There you have
a finished
triangle
- 5)Draw a line from point B
to point C
- 4) Label this line C
- 3) Measure a 40° angle from point A
and draw a 4cm line
- 2) Label the ends A and B
- 1) Draw the longest side
using a ruler
- Draw a triangle with sides of 4cm and 6cm and an angle of 40°.
- ASA
- Draw a triangle with angles 40° and 70° and with a side of length 8 cm
- 1) Draw an 8cm line, this will
be the bottom of the
triangle
- 2) Label the ends A and B
- 3) Measure an angle of 40° from point
A. Draw a long line, label this C
- 4) Measure and draw an angle
of 70° from point B to the 40°
line
- 5) Rub out the excess line
- You have a
finished triangle
- You have a
finished triangle
- 5) Rub out the excess line
- 4) Measure and draw an angle
of 70° from point B to the 40°
line
- 3) Measure an angle of 40° from point
A. Draw a long line, label this C
- 2) Label the ends A and B
- 1) Draw an 8cm line, this will
be the bottom of the
triangle
- Draw a triangle with angles 40° and 70° and with a side of length 8 cm
- SSS
- Draw a triangle with side lengths of 3cm, 5cm and 6cm
- 1) Draw the longest side,
a 6cm line
- 2) Label the ends A and B
- 3) Open the compasses to 5cm, put your
compass on point A and draw an arc
above the 6cm line
- 4) Open the compass to 3cm, put
your compass on point B and draw
an above the 6cm line
- 5) Join the arc to points A
and B, using a ruler
- You have a
finished triangle
- You have a
finished triangle
- 5) Join the arc to points A
and B, using a ruler
- 4) Open the compass to 3cm, put
your compass on point B and draw
an above the 6cm line
- 3) Open the compasses to 5cm, put your
compass on point A and draw an arc
above the 6cm line
- 2) Label the ends A and B
- 1) Draw the longest side,
a 6cm line
- Draw a triangle with side lengths of 3cm, 5cm and 6cm
- SAS
- Equipment needed to construct triangles
- Compass
- Ruler
- Pencil
- Protactor
- Compass
- Loci
- Farmer Smith has tied a cow around a post on
a rope 4 m long. What the locus of the cow as
it moves around the post?
- 4m, it will stay the same all
the way round the circle
- 4m, it will stay the same all
the way round the circle
- A flowerbed runs along the grass
between A and B. The edge of the
flowerbed is 1 m from the grass. How
would you draw an accurate diagram
showing the flowerbed, using a scale of 1
cm:1 m?
- Draw a line parallel to AB 1 cm
from AB. Shade in the area
between this line and the line AB
- The edge of the flowerbed
is the locus from the line
AB, because it is at a set
distance from the line
- The edge of the flowerbed
is the locus from the line
AB, because it is at a set
distance from the line
- Draw a line parallel to AB 1 cm
from AB. Shade in the area
between this line and the line AB
- Farmer Smith has tied a cow around a post on
a rope 4 m long. What the locus of the cow as
it moves around the post?
- Constructing the
perpendicular from a point
to a line
- 1.Open a pair of compasses so
the distance is slightly longer
than the distance from the
point to the line. Place the
compass at the point and draw
two arcs, crossing the line
either side of the point
- 2. Put the compass and the
first point on the line,
point A and draw an arc
below the line. Repeat
from point B without
changing the width of
your compass so the arcs
cross to create point C.
- 3. Place a ruler between the
point and C. Use a ruler to
connect the point to the line.
The line is at a right angle to AB.
- 3. Place a ruler between the
point and C. Use a ruler to
connect the point to the line.
The line is at a right angle to AB.
- 2. Put the compass and the
first point on the line,
point A and draw an arc
below the line. Repeat
from point B without
changing the width of
your compass so the arcs
cross to create point C.
- 1.Open a pair of compasses so
the distance is slightly longer
than the distance from the
point to the line. Place the
compass at the point and draw
two arcs, crossing the line
either side of the point
- Constructing the perpendicular
from a point on the line
- 1. P is a point on a line.
Construct a perpendicular at P.
- 2. Put the compass point at P.
Draw two arcs crossing the
line either side of P.
- 3. Put the compass point at A the
first point on the line and draw
an arc below the line. Repeat
from point B without changing
the width of your compass so
the arcs cross to create point C.
- 4. Use a ruler to connect point P to
where the two arcs cross, at C. The
line PC is at a right angle to AB.
- 4. Use a ruler to connect point P to
where the two arcs cross, at C. The
line PC is at a right angle to AB.
- 3. Put the compass point at A the
first point on the line and draw
an arc below the line. Repeat
from point B without changing
the width of your compass so
the arcs cross to create point C.
- 2. Put the compass point at P.
Draw two arcs crossing the
line either side of P.
- 1. P is a point on a line.
Construct a perpendicular at P.
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