TODAY IN GEOMETRY… Group POP QUIZ

Learning Target 1: 5.1 Use properties of mid segments of triangles to calculate lengths of sides

Learning Target 2: 5.5 You will find possible lengths for a triangle

Independent Practice

HW ALL DUE FRIDAY!

POP QUIZ:

You have 20 minutes to complete the warm up. Once completed turn in into the TURN IN BOX!

DISCOVERING MIDSEGMENT:

𝐴

𝐵𝐶

Find the midpoint of :

From draw a parallel line to

Calculate and :

What do you discover?The segment formed by the midpoint is half the length of the parallel segment.

𝐷𝐸

MIDSEGMENT THEOREM: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.

𝐴 𝐶

𝐵

𝐷 𝐸

𝑈 𝑉

𝑅

3. If the perimeter of , find the perimeter of .

4. If and , what is ?

𝑇𝑊

𝑆

1. If , find .

2. If , find .

FIGURE PLACEMEMT FOR A RECTANGLE: It is easiest to find lengths of horizontal and vertical segments and distances from , so place one vertex at the origin and one or more sides on an axis.

(h ,𝑘)(0 ,𝑘)

(0 ,0) (h ,0)

Let represent the length and represent the width.

FIGURE PLACEMENT FOR TRIANGLES: It is easiest to find lengths of horizontal and vertical segments and distances from , so place one vertex at the origin and one or more sides on an axis.

Notice that you need three different variables.

( 𝑓 ,𝑔)

(𝑑 ,0)(0 ,0)

HOMEWORK #1:

Page 298: 3-15, 24-27

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

𝑏𝐴𝐵 𝐵𝐶 𝐴𝐶¿ ¿

𝒔𝒊𝒅𝒆𝒃𝒊𝒔𝒕𝒉𝒆 𝒍𝒐𝒏𝒈𝒆𝒔𝒕 𝒔𝒊𝒅𝒆

𝒔𝒊𝒅𝒆𝒄 𝒊𝒔𝒕𝒉𝒆 𝒔𝒉𝒐𝒓𝒕𝒆𝒔𝒕 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

𝑥1. 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

ALL HW DUE FRIDAY!