Idiot\'s Guides Basic Math and Pre-Algebra

172 Part 3: The Shape of the World

If a triangle has an obtuse angle, an angle greater than 90r, it’s called an obtuse triangle.

The altitude of an obtuse triangle will often fall outside the triangle.

If a triangle has a right angle, it’s called a right triangle. We’ll take a closer look at right triangles

in the next section.

Acute triangle

Acute

angle

Acute

angle

Acute

angle

Obtuse triangle

Obtuse

angle

Right triangle

Leg

Leg

Hypotenuse

WORLDLY WISDOM

Obtuse triangles can only have one obtuse angle, and right triangles can only have

one right angle. The three angles of a triangle add up to 180r. If one angle is already

90 r or more, there’s 90r or less for the other two. They’ll have to be acute.

CHECK POINT

6. 'RST is isosceles with RS = ST. If m’SRT = 39r, then m’STR = __.


7. In right triangle 'ABC, AB BC and m’C is 19r. Find m’A.


8. True or False: If m’P = 17r and m’Q = 25r, then 'PQR is an acute triangle.


9. If m’P = 17r and m’Q = 25r, then the longest side of 'PQR is side __.


10. If the vertex angle of an isosceles triangle measures 94r, then the base angles
    measure __.

Right Triangles

Right triangles are triangles that contain one right angle, and they pop up all over the place.

When someone wants to build something that stands up vertically, they’ll often add a slanting

support to create a right triangle. Every time you draw an altitude in any triangle, you create two

right triangles. The right triangle is the one in which a side can also be an altitude.

In a right triangle, the two sides that meet to form the right angle are called the legs, and the

third side, opposite the right angle, is called the hypotenuse. The hypotenuse of a right triangle is

always the longest side because it’s opposite the right angle, the largest angle of the triangle.