Transcript Right angled triangles

CONTENT
and LANGUAGE
INTEGRATED
LEARNING
• You learn content….. MATHS
• You practice language in a specific
context…..
Let’s talk about…. ANGLES
What is an angle?
• Angle: the inclination to one
another of two straight lines that
meet.
• The point at which two lines meet is
called the vertex of the angle
(plural: vertices);
• the two straight lines are called
sides
Look at these different types of
angles and remember their
names:
Right angle: measures 90 degrees
(its sides are perpendicular)
Straight angle:
measures 180 degrees
(its sides lie on the same straight line)
a straight angle equals two right angles
Acute angles: measure less than 90°
(i.e. less than a right angle)
Obtuse angles: measure more than 90° but
less than 180°
(i.e. is greater than a right angle but less than a
right one)
• Angles are complementary
(or complements of one
another) if together they
equal a right angle.
• Angles are supplementary
(or supplements of one
another) if together they
equal a straight angle
(a and b are also
adjacent)
a
b
a
b
TRIANGLES
A triangle is a polygon with
three sides and three angles
In a triangle:
• we use capital letters for the vertices
• we name the opposite side of each vertex with the
same letter in small letters.
• we name the angles with Greek letters (a, b, g)
corresponding to the vertices A, B, C
The triangle on the right is the ABC
triangle
(e.g. side c is the opposite side of angle g;
angles a and b are adjacent to side c)
g
C
b
a
b
A a
c
B
Look at these
properties of triangles:
• there is a connection between the length
of the sides and the size of the angles:
The side opposite to the bigger angle is
longer, the same with the small one
• The sum of two sides is always bigger than
the remaining side
• The three angles always add to 180°
Activity:
g
Complete:
C
b
(refer to ABC triangle)
a
b
A a
c
a<c
a<…+…;
 …………
b<…+…
a + b + g = ………°
< ………..
B
How many types of
TRIANGLES?
There are three special names given to triangles
that tell how many sides (or angles) are equal:
scalene, isosceles, equilateral
( classification of triangles according to sides)
Triangles can also have names that tell you what
types of angles are inside:
acute, right, obtuse
( classification of triangles according to angles)
Types of triangles
Equilateral
Isosceles
triangle
triangle
By
their
sides
By
their
angles
A triangle having
all three sides of
equal length
A triangle having
two sides of the
same length
Acute
triangle
Right triangle
A triangle having
all acute angles
(right angled t.)
Scalene
triangle
A triangle
having all three
sides of
different length
Obtuse
Triangle
A triangle
A triangle having having an obtuse
a right angle
angle
Now answer to these questions:
a)
Does a triangle with two obtuse angles exist?
b)
What is the size of the angles in an equilateral triangle?
c)
If the vertex angle ( = the angle which is opposite to
the base) of an isosceles triangle is 100°, what is the
size of the remaining angles? How can you classify the
triangle in another way?
d) What type of triangle is the
grey one?
Example of answer:
“the grey triangle is …………… because it has an ……… angle; it has also two
…… sides, so/therefore it is an ……………… triangle
RIGHT ANGLED
TRIANGLES
• The side opposite to the right angle is
called “hypotenuse” and it is the longest
side
• The other two sides are called “legs”
the hypotenuse is ….
the legs are …… and ……
The inner acute angles add to 90, so they are ………………….
The right angled triangle is one of
the most useful shapes in all of
mathematics!
A right triangle can be isosceles; it is called
isosceles right angled triangle
 The size of the acute angles in this type of right
triangle is always ……… °
(try to explain why)
 We can obtain two equal isosceles right angled
triangle if we draw a diagonal of a square
(in another way: a square can be divided by a diagonal
into two isosceles right triangles, that are equal
OR: a square is formed by two equal isosceles right
triangles, joined by the hypoyhenuse)
Next lesson:
The Pythagorean Theorem!!
NAMING POLYGONS:
Look at these shapes and find the right name among those
written on the bottom of the slide
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