Applying 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.
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.
Holt McDougal Geometry
Applying Special Right Triangles
Holt McDougal Geometry
Applying Special Right Triangles
Example 1A: Finding Side Lengths in a 45°- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
By the Triangle Sum Theorem, the
measure of the third angle in the
triangle is 45°. So it is a 45°-45°90° triangle with a leg length of 8.
Holt McDougal Geometry
Applying Special Right Triangles
Example 1B: Finding Side Lengths in a 45º- 45º- 90º
Triangle
Find the value of x. Give your
answer in simplest radical form.
The triangle is an isosceles right
triangle, which is a 45°-45°-90°
triangle. The length of the hypotenuse
is 5.
Rationalize the denominator.
Holt McDougal Geometry
Applying Special Right Triangles
Check It Out! Example 1a
Find the value of x. Give your answer in
simplest radical form.
By the Triangle Sum Theorem, the
measure of the third angle in the
triangle is 45°. So it is a 45°-45°90° triangle with a leg length of
x = 20
Holt McDougal Geometry
Simplify.
Applying Special Right Triangles
Check It Out! Example 1b
Find the value of x. Give your answer in
simplest radical form.
The triangle is an isosceles right
triangle, which is a 45°-45°-90°
triangle. The length of the
hypotenuse is 16.
Rationalize the denominator.
Holt McDougal Geometry
Applying Special Right Triangles
Example 2: Craft 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.
Jana needs a 45°-45°-90° triangle with a hypotenuse
of 36 + 10 = 46 inches.
Holt McDougal Geometry
Applying Special Right Triangles
Check It Out! Example 2
What if...? Tessa’s other dog is wearing a
square bandana with a side length of 42 cm.
What would you expect the circumference of
the other dog’s neck to be? Round to the
nearest centimeter.
Tessa needs a 45°-45°-90° triangle with a
hypotenuse of 42 cm.
Holt McDougal Geometry