Intro to Geometry

Day 3

Segments and Their Measures

Consider the following map showing the route between Nashville, TN and Birmingham, AL:• Athens, AL is 101 miles south of Nashville and 95 miles north of Birmingham.

•What is the distance from Nashville to Birmingham?• Leaving Nashville and heading to Birmingham, you make a pit stop after 72 miles. How many miles do you have left to drive?• If you drive the average speed limit (65 mph), how long will it take to get from Nashville to Birmingham? (Disregard any time to stop)•You take the scenic route home which is 303 miles, but the average speed limit is 75 mph. Which was the quickest route?

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

If AB + BC = AC, then B is between A and C

A B C

AB

AC

BC

Example 1:

Given line segments AD = 18, AC = 6, and

AB = BC, find the following lengths:

a.BC

b.BD

A B C D

Measuring Distance with a Ruler

On a piece of graph paper, consider the grids to represent city blocks and place two boxes to represent a school and a house. (Feel free to get creative)

Trade papers with a neighborFind the distance you would have to walk home

if you stayed on the sidewalks (grids)Find the distance you would walk if you cut

through the yards directly from school to home. (diagonal)

Example 2:

Find the length of the following line segments.KLLM

M(0,-1)

K(-2,2)

L(-2,-3)

On the map, the city blocks are 410 feet apart east-west.

A. Find the walking distance between C & D

B. Find the diagonal distance between C & D

C(0, 740)

D(2050, -370)

Homework

Pg. 21-23#24 – 34 even, 48, 50, 52

Distance Formula and Pythagorean Theorem PracticeDraw a coordinate plane. On it draw a

diagonal line segment with endpoints on intersections of the grid paper. Label the endpoints.

Trade with a neighborUse either the distance formula or the

Pythagorean theorem to find the length of the line