1. 7.4 Special Right Triangles
Hubarth
Geometry

2. Triangle Theorem
Side-angle Correlation 45 x 45 x

3. Ex 1 Find the Hypotenuse Length
Find the length x of the hypotenuse in the triangle shown
at the right. 3 3 45 x
Solution

4. Ex 2 Find Leg Length
Find the length x of each leg in the triangle. 45 x 45 x
Solution

5. 45-45-90 Triangle Theorem Substitute. Ex 3 Standardized Test Practice
By the Corollary to the Triangle Sum Theorem, the triangle is a triangle. o o o
hypotenuse = leg 2
Triangle Theorem
= 25 2 WX
Substitute.
The correct answer is B.

6. Triangle Theorem 30 2x 60 x

7. Ex 4 Find Hypotenuse Length
In the triangle, the length of the shorter leg is given.
Find the length of the hypotenuse. 60 12 30
Solution
The side opposite the 30 is the shorter leg.

8. Ex Triangle
Find the values of x and y. Write your answer in simplest radical form.
STEP 1
Find the value of x.
longer leg = shorter leg 3
9 = x 3 9 3
= x
STEP 2
Find the value of y.
hypotenuse = 2 shorter leg 9 3
= x
𝑦=2∙3 3 =6 3 9 3
= x 3
= x

9. Practice 2. x x 1. 45 x 4 45 45 8 3.
x=14 4. 30 x 30 42 y 60 7 60 x