TODAY IN GEOMETRY…

Learning Target: 5.5 You will find possible lengths for a triangle

Independent Practice

ALL HW due Today!

Triangle inequalities:

The longest side of a triangle is opposite the largest angle.

The smallest side of a triangle is opposite the smallest angle.

𝐴

𝐵

𝐶

𝑎𝑐

𝑏

𝐴𝐵 𝐵𝐶 𝐴𝐶¿ ¿𝒔𝒊𝒅𝒆𝒃𝒊𝒔𝒕𝒉𝒆 𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

𝒔𝒊𝒅𝒆𝒄 𝒊𝒔𝒕𝒉𝒆𝒔𝒉𝒐𝒓𝒕𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

PRACTICE: List the sides of in order from shortest to longest.

𝑅

𝑆

𝑇40 °

101 °

39 °

𝑅𝑆 𝑆𝑇 𝑅𝑇¿ ¿

PRACTICE: List the angles of in order from smallest to largest.

𝑅

𝑆

𝑇

2420

27

∠𝑇 ∠𝑅 ∠𝑆¿ ¿

TRIANGLE INEQUALITY THEOREM: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

𝐶

𝐵

𝐴

PRACTICE: A triangle has one side of length 12 and another of length 8. Describe all possible lengths of the third side.Find the range of values that the missing side can be:

𝑥

12

8 812

𝑥

1. Smallest value of the missing side can be found by subtracting the two given sides.

2. Greatest value of the missing side can be found by adding the two given sides.

Possible lengths , ex. 5, 6, 7, 8, 9, …, 20

PRACTICE: Is it possible to construct a triangle with the sides ?

1. Smallest possible value can be found by subtracting the two largest numbers.

2. Greatest possible value can be found by adding the two smallest numbers.

YES, IT IS POSSIBLE TO CONSTRUCT THIS TRIANGLE!

Check smallest given side….3

Check greatest given side….9

HOMEWORK #2:

Pg. 331: 6-13, 16-23, 33

If finished, work on other assignments:

HW #1: Pg. 298: 3-15, 24-27