Metric Relations in Right Triangles

Lesson 1 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

Reminder: Similar Triangles Corresponding angles are congruent AND Corresponding sides are proportional in length Minimum Conditions: AA SAS 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

Class work and Homework Activity 1: Birds of a feather stick together!

Lesson 2 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

hypotenuse 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

Everyone draw another right angle triangle and name it Add the altitude Label all parts of the triangles created

Geometric Properties Using the lengths of the corresponding sides of the triangles formed, we can determine the ratios and from this determine certain geometric properties

Property 1 Information we have or need: 1. Measurement of leg 2. Measurement of projection 3. Measurement of hypotenuse

Property 1: leg leg proj proj

Property 1: leg leg proj proj

Class work and homework Worksheet hand out on Property 1

Lesson 3 Correct work on property 1

Property 2 Information we have or need: 1. Altitude 2. 2 segments that determine hypotenuse i.e. projections

Property 2: altitude proj proj

Class work and Homework Worksheet on Property 2

Lesson 4

Property 3 Information we have or need: 1. Hypotenuse 2. Altitude 3. Length of legs

Property 3: leg leg altitude hypotenuse

Property 3: Textbook Definition and formula 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.

Class work and homework Hand out on property 3

Lesson 5 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!!!

Property 4 You already know it: Pythagorean theorem leg² + leg² = hypotenuse²

Class Work and Homework Visions page 182, numbers 1,2,3,4