Geometry Warm-Up1/31/12  Find the value of x x x

Perfect Squares Quiz

Sec 8.3: Special Right Triangles Geometry January 31, 2012

Special Right Triangles  Special Right Triangles Triangles whose angles measures are either 45  -45  -90  or 30  -60  -90 .

45  -45  -90  Triangle  Special Relationships Because you have two 45  angles, the two legs are congruent. The hypotenuse is √2 times as long as each leg  Hypotenuse = √2 ● leg

30  -60  -90  Triangles  Special Relationships Because the two acute angles have different measures, you have a long leg and a short leg The hypotenuse is twice as long as the short leg and the long leg is √3 times as long as the short leg.  Hypotenuse = 2 ● short leg  Long Leg = √3 ● short leg

Example 1  Find the value of x. Hypotenuse = √2 ● leg x = √2 (7) x = 7√2

Example 2  Find the values of s and t. Long leg = √3 ● short leg 9 = √3 (s) 9√3 = s 3 3√3 = s Hyp = 2 ● short leg t = 2 (3√3) t = 6√3