Transcript Metric Relations in Right Triangles




Take the following 2 pages of notes
Create a triangle and proof the triangles are
similar after adding an altitude
Work in Visions textbook 1 page 179

By drawing the altitude
from the right angle of
a right triangle, three
similar right triangles
are formed
C
△ABC∼△ACD∼△ADB
Corresponding angles
are congruent
AND
 Corresponding sides
are proportional in
length

Minimum Conditions:
1. AA
2. SAS
3. SSS

Activity
Take 10 minutes.
Use graph paper
Draw a right triangle
Draw the altitude from the right angle
Prove that 3 similar triangles are formed

Activity 1: Birds of a feather stick together!


Finish and correct Birds of a feather
Everyone create a triangle as on next slide
and write in the names of each part of the
triangle created

The altitude to the
hypotenuse of a right
triangle forms two
triangles that are
similar to each other
and to the original
triangle.
leg
leg
projection

projection
hypotenuse



Everyone draw another right angle triangle
and name it
Add the altitude
Label all parts of the triangles created

Using the lengths of the corresponding sides
of the triangles formed, we can determine the
ratios and from this determine certain
geometric properties
Information we have or need:
1. Measurement of leg
2. Measurement of projection
3. Measurement of hypotenuse

leg
leg
proj
proj
projection
leg

leg
hypotenuse
leg
proj
projection
leg

leg
hypotenuse
leg
proj

Worksheet hand out on Property 1

Correct work on property 1
Information we have or need:
1. Altitude
2. 2 segments that determine hypotenuse i.e.
projections

altitude
proj
proj
projection
altitude

altitude
projection

Worksheet on Property 2
Information we have or need:
1. Hypotenuse
2. Altitude
3. Length of legs

leg
leg
altitude
hypotenuse
hypotenuse  altitude  leg  leg

In a right triangle, the
product of the length
of the hypotenuse and
its corresponding
altitude is equal to the
product of the lengths
of the legs.

Hand out on property 3





Correct all homework
Go over the information to date
Draw and altitude within a right triangle
Label the parts
Write the properties 1-4. What is property 4?
You already know it!!!

You already know it: Pythagorean theorem
leg² + leg² = hypotenuse²

Visions page 182, numbers 1,2,3,4