Download Angle Construction

An angle is formed when two rays meet at a point called the vertex.
Angles are usually measured in degrees using a protractor. Angle
measures range from 0° to 360°.
Angles are classified according to their size in degrees.
Acute Angle
Right Angle
measure is between measure is 90°
0° and 90°
Obtuse Angle
Straight Angle
measure is between measure is 180°
90° and 180°
Reflex Angle
measure is between
180° and 360°
1. Identify the following angles as acute, right, obtuse,
straight, or reflex.
2.
a)
Identify the type of angle:
68°
e) 180°
b) 215°
c) 91°
d) 32°
f) 99°
g) 193°
h) 265°
Complementary Angles: two angles that have measures (size) that add up
to 90°
Supplementary Angles: two angles that have measures that add up to 180°
Opposite Angles: two angles that are opposite each other have the same
measure
Congruent Angles: Two angles with the same measure are referred to as
congruent. For example, opposite angles are congruent.
Examples:
3.
Given each of the following angles, determine the size of the complement
and/or the size of the supplement (if they exist).
a)
75°
b)
43°
c)
103°
d)
87°
e)
3.
300°
Sort the following angles into pairs of complementary and supplementary :
1 = 42°
5 = 121°
2 = 107°
6 = 31°
3 = 59°
7 = 19°
4 = 48°
8 = 73°
Curriculum Outcomes:
10E2.AC.1. demonstrate an understanding of angles, including acute, right,
obtuse, straight, and reflex, by: drawing, replicating and constructing,
bisecting, and solving problems
Assignment: Angles
To bisect something is to cut it into two equal parts.
An angle is bisected by a ray that divides it into two angles of
equal measure. The ray that divides the angle is called an
angle bisector.
Perpendicular lines are two lines that form a right angle.
Examples:
1.
2. Estimate the size of the angle shown below and then
bisect it.
3. By inspections, determine which of the following lines are
perpendicular..
4. The size of an angle is the same as the supplement of the
bisected angle, what is the angle?
Curriculum Outcomes:
10E2.aC.1. demonstrate an understanding of angles, including acute, right,
obtuse, straight, and reflex, by drawing, replicating and constructing,
bisecting, and solving problems
Assignment: Angle Bisectors and
Perpendicular Lines
Definitions:
transversal: a line that intersects two or more lines
corresponding angles: two angles that occupy the same relative
position at two different intersections
opposite angles: angles created by intersecting lines that share only a
vertex
interior angles: on the same side of the transversal: these angles are
supplementary (different intersections)
exterior angles: on the same side of the transversal: these angles are
supplementary (different intersections)
alternate interior angles: angles in opposite positions between two
lines intersected by a transversal and also on alternate sides of the
same transversal (different intersections)
alternate exterior angles: angles in opposite positions outside two lines
intersected by a transversal (different intersections)
If two parallel lines are intersected by a transversal:
• the alternate interior (exterior) angles are equal;
• the corresponding angles are equal;
• the interior (exterior) angles on the same side of the
transversal are supplementary.
If you are given two lines cut by a transversal:
• alternate interior (exterior) angles are equal; OR
• corresponding angles are equal; OR
• interior (exterior) angles on the same side of the transversal
are supplementary;
then you can conclude that the lines are parallel.
Examples:
1.
Consider the diagram below, in which ℓ1 is parallel to ℓ2. What are the
measures of the three indicated angles? Explain how you reached your
answers.
2. Given the diagram below, identify all the pairs of parallel lines and
explain your selection.
Curriculum Outcomes:
10E2.aC.2. solve problems that involve parallel, perpendicular, and
transversal lines, and pairs of angles formed between them.
Assignment: Parallel Lines and Transversals
Important Note:
Non – parallel lines follow the same definitions as parallel lines with the
exception that we cannot determine the size of the angles just their
positioning.
Example:
1.
Consider the diagram below: t is a transversal that intersects ℓ1 and ℓ2.
• ∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7 are pairs of corresponding angles.
• ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8 are pairs of opposite angles.
• ∠3 and ∠5, ∠4 and ∠6 are pairs of alternate interior angles.
• ∠2 and ∠8, ∠1 and ∠7 are pairs of alternate exterior angles.
• ∠3 and ∠6, ∠4 and ∠5 are pairs of interior angles on the same side of the transversal.
• ∠1 and ∠8, ∠2 and ∠7 are pairs of exterior angles on the same side of the transversal.
2.
Identify each of the following and specify which line and transversals
you are using.
a) an interior angle on the same side of the transversal as ∠6
b) an angle corresponding to ∠2
c) an angle corresponding to ∠4
d) an alternate interior angle to ∠4
3.
In the diagram below, measure and record the sizes of the angles.
Identify pairs of equal angles and state why they are equal.
Curriculum Outcomes:
10E2.aC.2. solve problems that involve parallel, perpendicular, and transversal lines,
and pairs of angles formed between them.
Assignment: Non – Parallel Lines and
Transversals
Rotations:
●
●
●
a rotation is a transformation in which a figure is turned or rotated
to rotate a figure, you need to know the amount and direction of
the rotation as well as the point of rotation (called the turn centre)
we will look at 90°, 180°, and 270° rotations