Mrs. McConaughy GEOMETRY 1

Introduction to Proof: Drawing Conclusions, part 2b

Objectives: Objectives:

To draw conclusions about To draw conclusions about angles using given angles using given informationinformation

To use the substitution and To use the substitution and transitive propertiestransitive properties

Mrs. McConaughy GEOMETRY 2

Before we start, recall:

Measures are equal

Parts are congruent

m BAC = m DEF BAC DEF

m AB = m CD

AB = CD

AB CD

Mrs. McConaughy GEOMETRY 3

If we know certain things about angles, we can discover other things about

them.

B105

A

If m A = 105 and m B = 105, then __________________________________.

If m A = m B, then ____________.

105

m A = m B

A B

Mrs. McConaughy GEOMETRY 4

Example 1

If HJ bisects GHI, then ______________. If GHI IHJ, then ________________.

G H

J

I

Mrs. McConaughy GEOMETRY 5

Drawing ConclusionsDrawing Conclusions

If X Y and Y Z, then _______________________________.

If X Z, then __________________________________.

Mrs. McConaughy GEOMETRY 6

Transitive Property of Congruence

If X Y and Y Z, then _____.

If AB CD and CD EF,___________.

Example 2

If AOB BOCBOC and BOCBOC COD, which other angles are congruent?

Mrs. McConaughy GEOMETRY 7

Substitution Property of Equality

If m A = m B, then A can be substituted for B in any equation..

If AB = CD, then AB can be substituted for CD in any equation.

Mrs. McConaughy GEOMETRY 8

Example 3

Given m T = 53 and m V = 53, by the substitution property, we can conclude ________________________________.

Therefore, ________________________________.

5353

T V

Mrs. McConaughy GEOMETRY 9

Example 4

If GH = KL and KL = RT, then __________________________.

You will use the transitive property and substitution property in showing relationships between angles or segments.

Mrs. McConaughy GEOMETRY 10

Reading in GeometryGeometry

Completion. You may need to draw and label diagrams to complete the statements which follow. If necessary, use the word bank below:

midpointmidpoint

conclusionsconclusions

midpointmidpoint

bisectsbisects

informationinformation

picturespictures

Mrs. McConaughy GEOMETRY 11

Geometry often involves using information that is known to discover other _______________.

This is called drawing __________.

For example, if you know that AB _____ CAD, then you know that

CAB BAD.

Similarly, if P is the _________ of AB, then you know that AP PB.

Mrs. McConaughy GEOMETRY 12

Drawing Conclusions WS

Homework Assignment