Download 6_Perpendicular_bisector

Starter A
1)Angle bisect YZW
2)Angle Bisect XWZ
3)Mark where the angle bisectors meet point P
4)Measure the distance ZP in mm.
X
Y
W
Z
Starter B
1) Construct an equilateral triangle with sides of 7cm. Label it ABC
2) Angle bisect angle ABC. Continue the angle bisector until it
touches line AC. Label this point P
3) Angle bisect angle APB and CPB.
Continue the angle bisectors until
they touches the sides of the triangle.
Label these points Q and R
4) Measure the distance
QR in mm. QR = ______ mm
0
1
2
3
4
5
6
7
Measuring angles
Skills:
Measure and draw angles using a protractor.
Measuring angles
1) Put protractor “gun sight” carefully on the angle point…
2) And line up a “0” on one line
3) Read off the angle (use the correct set of numbers)
Measure these angles
B = _____
C= _____
A = _____
Measuring angles
Draw an angle
1) Rule a line (any length)
2) Put protractor “gun sight” carefully on one end of the line…
3) And line up a “0” on one line
4) Mark the angle needed (use the correct set of numbers)
5) Rule in the angle line
B =115°
A = 35°
C= 70°
1
5
4
3
2
0
1
2
3
4
5
Constructing triangles A
Skills:
Construct triangles given sides and angles.
Given 3 sides lengths
1) Rule and measure the longest side
2) Set compass length of second side and arc.
3) Set compass to the length
of the third side and arc again
so the arc’s cross. Mark this point
4) Rule in the triangle sides
Construct a triangle with side
lengths 3cm, 4cm and 5cm
4cm
5cm
3cm
0
1
2
3
4
5
1
5
4
3
2
0
1
2
3
4
5
Constructing triangles B
Given 2 sides and 1 angle
1) Rule the longest side (correct length)
2) Measure the angle with a protractor
3) Rule the second side (correct length)
4) Rule in the third side
Construct a triangle with side
lengths 5cm, 4cm and a
45° angle between them
4cm
45°
5cm
0
1
2
3
4
5
0
1
2
3
4
5
Constructing triangles C
Given 1 side and 2 angles
1) Rule and measure the side length
0
1
2
3
4
5
2) Measure the angle to each of the other sides.
Rule the sides in until they cross.
Eg: 1) Construct a triangle with side length
BC 5cm, and a 40° and 50° angles
2) Measure the sides AB = ____
AC = ____
3) Measure the angle BAC = ____
Eg: 1) Construct a triangle with side length PQ 3cm,
and a 30° and 120° angles
2) Measure the sides PR = ___
QR = ____
3) Measure the angle PRQ = ____
30°
P
R
120°
3cm
Q
Perpendicular bisector
Skill: Construct perpendicular bisectors.
Definition: ___________________________________
Text Information: Beta pg. 224
Practice: Beta pg. 226 Ex 16.1
Must
B
A
Construct the perpendicular bisector to the line AB
B
A
Note that line AB is now cut in half at 90°
B
A
Perpendicular line from point
Skills: Construct perpendicular lines from a point near a line.
Construct a line passing through point P
which is also perpendicular the line DE
Text Information: Beta pg. 226
Practice: Beta pg. 228 Ex 16.2
Must #1 to 3
P
Note that line DE is now cut at 90°
E
D
Put compass point at P
Adjust the compass to reach just over
line DE so the arc cuts the line twice
Mark these points A and B
Now construct the perpendicular bisector
of line AB as before.
.
P
D
.
E
Perpendicular line from
Steps: Construct perpendicularpoint
lines from a point on a line.
Construct a line passing through point P
which is also perpendicular the line GH
Text Information: Beta pg. 227
Practice: Beta pg. 228
Ex 16.2 Must #4 to 6
H
P
G
Put compass point at P
Adjust the compass so the arc cuts the
line GH twice.
Mark these points A and B
Now construct the perpendicular bisector
of line AB as before.
G
Note that line GH is now crossed at 90°
.
H
P
.
Find the circumcircle
Given any triangle construct a circle which will pass through all
three corners of the triangle.
Steps:
1) Rule a neat large triangle.
2) Perpendicular bisect all three sides
3) Continue the perpendicular bisectors
until they intersect. Label this point P
4) Put compass point at P and construct a
circle passing through the corners of the circle.
Extension: Circumcircle
Given any triangle construct a circle which will pass through all
three corners of the triangle.
Extension: Centre of gravity
Given any triangle use construction to find the centre of gravity of
the triangle.
1) Rule a neat large triangle.
2) Perpendicular bisect all three sides. Don’t rule in the
perpendicular bisector, just mark the midpoint of the side.
3) Rule a line from a corner of the triangle to the middle of the
opposite side found in step 2).
4) Repeat step 3) for the other two corners of the triangle.
5) Where the three lines meet mark point P. This is the centre of
gravity (balance point of the triangle)
6) Repeat this on a piece of scrap paper. Carefully cut out the
triangle. Put a pen point on point at P see if the triangle balances.
Extension: The “altitude” is the line from a corner of a triangle which
intersects the opposite side at 90° Do all 3 altitudes of a triangle
meet?