This document discusses triangles and their classifications. It defines a triangle as a three-sided polygon with three interior angles that sum to 180 degrees. Triangles are classified based on their interior angles as acute, right, or obtuse triangles, or as equiangular triangles if the three angles are equal. They are also classified based on the lengths of their sides as scalene, isosceles, or equilateral triangles. Several triangle types such as right, obtuse, isosceles and equilateral triangles are defined. The hypotenuse of a right triangle is described as the side opposite the right angle. The Pythagorean theorem relating the sides of a right triangle is presented. The document concludes with a 10 question

1. The World of
Triangles
Conrado P. Macapinlac, Sr. High School
Mr. Carlo Justino J. Luna
www.iamcarloluna.blogspot.com

2. Triangles
A triangle is a 3-sided
polygon. Every triangle
has three sides and
three angles. When
added together, the
three angles equal 180°.

3. Classifications:
According to the interior angles:
1. Acute triangle
2. Right triangle
3. Obtuse triangle
4. Equiangular triangle
According to the number of congruent sides:
1. Scalene triangle
2. Isosceles triangle
3. Equilateral triangle

4. Acute Triangle
• An acute triangle
with three acute
interior angles.

5. Right Triangle
• A right triangle is a
triangle with one
right angle.

6. Obtuse Triangle
• An obtuse triangle is
a triangle with one
obtuse angle.

7. Equiangular
Triangle
• An obtuse triangle is
a triangle which has
three equal angles.

8. Scalene Triangle
• A scalene triangle is
a triangle with three
unequal sides.

9. Isosceles Triangle
• An isosceles triangle
is a triangle with two
congruent sides.

10. Equilateral
Triangle
• An equilateral
triangle is a triangle
with three congruent
sides.

11. The Hypotenuse
The hypotenuse of a right
triangle is the triangle's
longest side, i.e., the side
opposite the right angle.

12. Pythagorean theorem
For a right triangle with
legs a and b and
hypotenuse c, a2
+b2
=c2
.

13. Triangle Quiz
Please complete the
following quiz that
covers the information
that was just presented
to you.

14. Question 1
• If a triangle has
three unequal
sides, it is a
______ triangle.
– A) Scalene
– B) Obtuse
– C) Isosceles
• Answer:
– A) Scalene

15. Question 2
• A triangle which
has three equal
angles is a
______ triangle.
– A) Acute
– B) Equilateral
– C) Equiangular
• Answer:
– C) Equiangular

16. Question 3
• A triangle with (at
least) two equal
sides is a ______
triangle.
– A) Scalene
– B) Isosceles
– C) Congruent
• Answer:
– B) Isosceles

17. Question 4
• Two triangles
that are equal are
called ______
triangles
– A) Acute
– B) Obtuse
– C) Congruent
• Answer:
– C) Congruent

18. Question 5
• A triangle with all
three sides of
equal length is a
______ triangle.
– A) Equilateral
– B) Right
– C) Equiangular
• Answer:
– A) Equilateral

19. Question 6
• A triangle with an
angle of 90° is a
______ triangle.
– A) Acute
– B) Right
– C) Congruent
• Answer:
– B) Right

20. Question 7
• A triangle in
which all three
angles are less
than 90° is a
______ triangle.
– A) Right
– B) Acute
– C) Scalene
• Answer:
– B) Acute

21. Question 8
• A triangle in
which one of the
angles is greater
than 90° is a
______ triangle.
– A) Obtuse
– B) Isosceles
– C) Acute
• Answer:
– A) Obtuse

22. Question 9
• What is the
Hypotenuse of a
right triangle?
– A) The smallest
angle.
– B) The side
opposite the right
angle.
– C) The right
angle.
• Answer:
– B) The side
opposite the right
angle.

23. Question 10
• The Pythagorean
Theorem states
…
– A) πr2
– B) (a+b)2
/2=c
– C) a2
+b2
=c2
• Answer:
– C) a2
+b2
=c2

24. Question 11
• Use the
Pythagorean
Theorem to solve
the following:
– a = 5
– b = 12
– c = ?
• Answer:
– c = 13

25. Triangles
Conrado P. Macapinlac, Sr. High School
Mr. Carlo Justino J. Luna
www.iamcarloluna.blogspot.com