Unit 1.3a Segment Addition Postulate Amp Midpoint Theorem CP

8/10/2019 Unit 1.3a Segment Addition Postulate Amp Midpoint Theorem CP

1/17

Unit 1.3 - Segment and angle relationships1.3a Prove theorems involving the Segment Addition Postulate

1.3b Formal geometric constructions using a variety of tools and

methods to copy and bisect an angle

1.3c Prove theorems involving the Angle addition postulate

1.3d Prove theorems about angle pairs

1.3e Prove theorems involving parallel lines and transversals

1.3f Formal geometric constructions using a variety of tools andmethods to construct perpendicular lines.

Common Core State Standards for Mathematical Content Congruence G-CO

Prove geometric theorems[Focus on validity of underlying reasoning while using variety of ways of writing proofs]G-CO.9Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a

transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent;

points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints.

G-CO.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle;

bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a

line segment; and constructing a line parallel to a given line through a point not on the line.


2/17

1.3a Prove theorems involving the

Segment Addition Postulate

Postulate: Mathematical statement thatis accepted without proof


3/17


4/17

Segment Addition Postulate

If B is between A and C, then

AB + BC = AC.

A BC


5/17

Write a mathematic equation for FA using the

segment addition postulate.

What would the equation look like now?

FA =


6/17

1. If N is between M and P and

MN = 10, MP = 25, find NP

10

25


7/17

A flight from PVD to NYC is 143 miles

A flight from PVD to Washington DC is 355 miles

A flight from NY to Washington DC is _____ miles


8/17

Seg. Add. Post. Example

If J is between H and K and HJ=5x-3 , JK = 4x,

HK = 8x, find HJ, JK, HK

Ans: Draw a diagram


9/17

Example

M is between L and N. Find eachmeasurement if: LM = 4x+6 ,

LN = 5x+10

MN = 3x

4

4

82

10527

1054364

x

x

xx

xxx

LM + MN = LN

LM =4(4)+6 = 22

MN = 3(4)-4 = 8

LN = 5(4)+10 = 30


10/17

If U is between T and B, find the value of x

and the measure of if

TU= 4x1, UB = 2x -1, and TB = 5x

Explain all your work

TU


11/17

Ex: if DE=2, EF=5, and DE=FG,

find FG, DF, DG, & EG.

DE

F G

FG=2

DF=7

DG=9

EG=7


12/17

Write an expression for QR

13x + 25

8x+5

PR = PQ + QR13x + 25 = (8x+5) + QR

-8x-8x

5x + 25 = 5 + QR-5-5

5x + 20 = QR

QR =5x + 20


13/17

Segment bisectors

M is the midpoint of AB

MBAM

Segment AM is CONGRUENTto segment MB

Congruent segments: Segments that have the

same length

and AM = MB


14/17

M is the midpoint of . Find AM and MBAB

26


15/17


16/17

If M is the midpoint of ,

AM = 2x + 11, MB = 4x

5

Find the value of x and the measure of

AB

AB

2x + 11 4x - 5


17/17

CP Geometry

Assignment

In class assignment: Practice worksheet 1.3aSegment addition postulate & midpoint

theorem

Homework: Page 33: 22-25, 38-40,

Page 41: 15-23, 33-35

Unit 1.3a Segment Addition Postulate Amp Midpoint Theorem CP

Documents

Transcript of Unit 1.3a Segment Addition Postulate Amp Midpoint Theorem CP