This document defines and describes different types of triangles:
- Equilateral triangles have three equal sides and three equal angles.
- Isosceles triangles have at least two equal sides.
- Scalene triangles have no equal sides.
- Right triangles have one 90 degree angle.
- Acute triangles have all angles less than 90 degrees.
- Obtuse triangles have one angle greater than 90 degrees.
It also describes three theorems used to prove triangle congruence: SSS (three equal sides), SAS (two equal sides and the included angle), and ASA (two equal angles and one included side).
This slide show was prepared to help my fourth grade students understand and identify the different types of triangles and to help them with their homework.
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6. Types of Triangles
Equilateral triangle: A triangle with
three congruent (equal) sides and
three equal angles.
These marks indicate equality.
7. Types of Triangles
Isosceles triangle: A triangle with
at least two congruent (equal) sides.
8. Types of Triangles
Scalene triangle: A triangle that
has no congruent (equal) sides.
9. Acute Angled Triangles: Has all
angles more than (0 degree) and less
than (90 degree).
Types of Triangles
10. Types of Triangles
Right triangle: Has only one right
angle (90 degrees).
This box indicates a right
angle or a 90-degree angle.
11. Obtuse Angled Triangles: Has one
angles more than (90 degree) and
less than (180 degree).
Types of Triangles
One angle greater than 90
And less than 180 degree
12.
13. Congruence triangles are triangles that have the
same shape and the same size.
A
C
B
D
F
E
ABC DEF
When we say that triangles are congruent there are
several repercussions that come from it.
A D
B E
C F
AB DE
BC EF
AC DF
14. 1. SSS Congruency Theorem
3 pairs of congruent sides
Six of those statements are true as a result of the
congruency of the two triangles. However, if we need
to prove that a pair of triangles are congruent, how
many of those statements do we need? Because we are
working with triangles and the measure of the angles
and sides are dependent on each other. We do not
need all six. There are three special combinations that
we can use to prove congruency of triangles.
2. SAS Congruency Theorem
2 pairs of congruent sides and congruent
angles between them
3. ASA Congruency Theorem
2 pairs of congruent angles and a pair of
congruent sides
15. 1. SSS Congruency Theorem
3 pairs of congruent sidesA
B C
5
12
ABC DFE
D
FE
5
12
5 DFmABm
12 FEmBCm
13 DEmACm
16. 2. SAS Congruency Theorem
2 pairs of congruent sides and congruent
angles between them
G
H I
L
J K
7
70
70
mH = mK = 70°
GHI LKJ
7
5 LKmGHm
7 KLmHIm
17. The SAS Congruency Theorem does not work unless
the congruent angles fall between the congruent
sides. For example, if we have the situation that is
shown in the diagram below, we cannot state that the
triangles are congruent. We do not have the
information that we need.
G
H I7
50
Angles I and J do not fall in between sides GH and HI and
sides LK and KJ respectively.
L
J K
50
7
18. 3. ASA Congruency Theorem
2 pairs of congruent angles and one pair of
congruent sides.
M
N O
70 50
mN = mR
mO = mP MNO QRP
Q
R P
7050
7 RPmNOm
77
