Right tri sim day 1

GT Geometry Drill 3/7/14

Turn in HW on the bookshelfWhat is the geometric mean of

the two measurements?

GT Geometry Drill 3/7/14

Turn in HW on the bookshelfWhat is the geometric mean of

the two measurements? 1) 2 and 8 2) 16 and 13) 12 and 2

Objective•Students will explore the properties of similar right triangles so that they can find unknown sides.

Altitude to Hypotenuse

Altitude to Hypotenuse

Altitude to Hypotenuse• The altitude extending

from the hypotenuse to the right angle.

1

12

2d e

ha b

c

h

Example

a bd

c

Example

a bd

cd

da

ccb

Example

a bd

c

Example

a bd

cd

da

ccb

Example

a bd

c

Example

a bd

cd

da

ccb

Example

a bd

c

Example

a bd

cd

da

ccb

Example

a bd

c

Example

a bd

cd

da

ccb

Example

a bd

c

Example

a bd

cd

da

ccb

Right ∆ Similarity Theorem• The altitude to the hypotenuse

of a right triangle divides the triangle into 2 triangles that are similar to each other and the original triangle.

36

x

Solve for x

48

x

Solve for x

Corollary 1• 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.

•

h

d e

dh

= he

•Long-Long, Short-Short

h

d e

dh

= he

• Long-Long, Short-Short• The ratio of the longer legs is

equal to the ratio of the shorter legs

h

d e

dh

= he

•Solve for x:

x5

9

Example

5 8

x

5 = xx 8 x = ?

Corollary 2• 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.

Example

d e

hb

d + e = bb e

Example

3 1

x2

3 +1 = 22 1

Classwork•Assignment #78

Conclusion• 1) A right triangle can be

divided by its altitude so that…• 2) In your own words, state

what Long-Long, Short-Short means.