Download 7.3 Notes Name____________________ Similar Right Triangles

7.3 Notes
Name____________________
Similar Right Triangles and Geometric Mean
In the picture below are 3 similar triangles. Draw the 3 triangles separately and mark the
corresponding parts. Then, complete the proportions.
Δ ABC (big triangle)
Δ ABD (left triangle)
Δ CBD (right triangle)
#1 Compare !CBD to !ABD
#2 Compare !ABD to !ABC
#3 Compare !CBD to !ABC
AD
AD
CD
BD
=
CB
=
CD
AB
=
BC
=
AC
=
BC
The geometric mean of two numbers is the number x that satisfies
a
x
=
AB
x
b
=
AC
such that ab = x 2 .
In the figure above, the following are geometric means:
•
BD (the altitude) is the geometric mean between
____________ and ____________
•
AB (left leg) is the geometric mean between
____________ and ____________
•
BC (right leg) is the geometric mean between
____________ and ____________
Altitude Geometric Mean (Heartbeat): In a
Leg Geometric Mean (Boomerang): In a right
right triangle, the length of the altitude from
triangle, with an altitude drawn from right
the right angle is the geometric mean between
angle, the length of each leg is the geometric
the two segments that form the hypotenuse.
mean between the whole hypotenuse and the
segment of the hypotenuse that is adjacent to
the given leg. Find the exact value of the given variables.
1.
Find a.
3. Find w.
5.
Find AC and DB.
2.
Find x.
4. Find AD.