Transcript Similarity in Right Triangles LESSON 7-4 Additional Examples Find the geometric mean of 3 and 12.= x x Write a proportion. x2 = 36 Cross-Product Property x= Find the.

Similarity in Right Triangles
LESSON 7-4
Additional Examples
Find the geometric mean of 3 and 12.
3
= x
x
12
Write a proportion.
x2 = 36
Cross-Product Property
x=
36
Find the positive square root.
x=6
The geometric mean of 3 and 12 is 6.
Quick Check
HELP
GEOMETRY
Similarity in Right Triangles
LESSON 7-4
Additional Examples
Solve for x and y.
Use Corollary 1 of Theorem 7-3 (The length of the
altitude to the hypotenuse of a right triangle is the
geometric mean of the lengths of the segments of the
hypotenuse) to find x.
2
= 6
6
x
2x = 36
Write a proportion.
Cross-Product Property
x = 18
HELP
GEOMETRY
Similarity in Right Triangles
LESSON 7-4
Additional Examples
(continued)
Use Corollary 2 of Theorem 7-3 (The altitude to the
hypotenuse of a right triangle intersects it so that the
length of each leg is the geometric mean of the
length of its adjacent segment of the hypotenuse
and the length of the entire hypotenuse) to find y.
x
y
=
y
2+x
y
18
= 2 + 18
y
Write a proportion.
Substitute 18 for x.
y2 = 360
Cross-Product Property.
y=
Find the positive square root.
y=6
HELP
360
10
Write in the simplest radical form.
Quick Check
GEOMETRY
Similarity in Right Triangles
LESSON 7-4
Additional Examples
At a golf course, Maria drove her ball 192 yd straight toward
the cup. Her brother Gabriel drove his ball straight 240 yd, but not
toward the cup. The diagram shows the results. Find x and y, their
remaining distances from the cup.
Use Corollary 2 of Theorem 7-3 to solve for x.
x + 192
240
=
240
192
192(x +192) = 2402
192x + 36,864 = 57,600
192x = 20,736
Write a proportion.
Use the Cross-Product Property.
Use the Distributive Property.
Solve for x.
x = 108
HELP
GEOMETRY
Similarity in Right Triangles
LESSON 7-4
Additional Examples
(continued)
Use Corollary 2 of Theorem 7-3 to solve for y.
y
x + 192
= x
y
y
108 + 192
= 108
y
y
300
=
108
y
y2 = 32,400
y=
32,400
Write a proportion.
Substitute.
Simplify.
Use the Cross-Product Property.
Find the positive square root.
y = 180
Maria’s ball is 108 yd from the cup, and Gabriel’s ball is
180 yd from the cup.
Quick Check
HELP
GEOMETRY