Chapter 5
5-8 Applying Special Right
Triangles
Objectives
Justify and apply properties of 45°-45°90° triangles.
Justify and apply properties of 30°- 60°90° triangles.
Special right Triangles
A
diagonal of a square divides it into two
congruent isosceles right triangles. Since
the base angles of an isosceles triangle
are congruent, the measure of each
acute angle is 45°. So another name for
an isosceles right triangle is a 45°-45°-90°
triangle.
Special right triangle
A
45°-45°-90° triangle is one type of
special right triangle. You can use the
Pythagorean Theorem to find a
relationship among the side lengths of a
45°-45°-90° triangle.
Triangle theorem
Example
 Find
the value of x. Give your answer in
simplest radical form.
Example
 Find
the value of x. Give your answer in
simplest radical form
Example
 Find
the value of x. Give your answer in
simplest radical form.
Application
 Jana
is cutting a square of material for a
tablecloth. The table’s diagonal is 36
inches. She wants the diagonal of the
tablecloth to be an extra 10 inches so it
will hang over the edges of the table.
What size square should Jana cut to
make the tablecloth? Round to the
nearest inch.
Triangle theorem
A
30°-60°-90° triangle is another special
right triangle. You can use an equilateral
triangle to find a relationship between its
side lengths.
Example
 Find
the values of x and y. Give your
answers in simplest radical form.
Example
 Find
the values of x and y. Give your
answers in simplest radical form.
Example
 Find
the values of x and y. Give your
answers in simplest radical form.
Application
 An
ornamental pin is in the shape of an
equilateral triangle. The length of each
side is 6 centimeters. Josh will attach the
fastener to the back along AB. Will the
fastener fit if it is 4 centimeters long?
Application
 What
if…? A manufacturer wants to make
a larger clock with a height of 30
centimeters. What is the length of each
side of the frame? Round to the nearest
tenth.
Student Guided Practice
 Do
problems 1-8 in your book page372
Homework
 Do
problems 9-16 in your book page 372
Closure
 Today
we learned about special right
triangles
 Next class we are going to learned about
properties and attributes of polygons