McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
3. Special Right Triangles
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Exercise 40 Page 564

Start with recalling the properties of special right triangles.

Variable Value

Perimeter:

Practice makes perfect

Let's begin by reviewing the properties of special right triangles.

Triangle Triangle
In a triangle, the legs are congruent and the hypotenuse is times the length of a leg. In a triangle, the hypotenuse is times the length of the shorter leg and the longer leg is times the length of the shorter leg.

Now let's take a look at the given picture. We will name the missing vertices.

First of all, we can see that and are congruent as is a rectangle. Therefore, the value of is also

Since is a triangle, the length of the hypotenuse is times the length of the shorter leg.
The value of is We can add this information to our picture.
Next, let's recall that in a triangle the length of the longer leg is times the length of the shorter leg.
The value of is

Let's notice that and are congruent. Therefore, the length of is As we can see, is a triangle, so the length of is also and the length of is

Finally, as we found all side lengths of trapezoid we can evaluate its perimeter,
The perimeter of trapezoid is