Warm-up

12/3 = 4 2 + 2 = 2 + 2 or 22 = 2 + 2

26 – 63 = 1 63 – 62 = 1

Agenda

Chapter 1 Test Review Homework Review Concept Review Section 2-3 Deductive Reasoning

Homework

Chapter 1 Test

1) Plot the following points: A (11, 14), B (-13, -7), C (-8, 11), D (8, -7)

AB’s midpoint is (-1, 7/2) and its length is 31.89.

CD’s midpoint is (0, 2) and its length is 24.08.

AB’s slope is 7/8 and CD’s slope is -9/8.

The two lines are not perpendicular.

Chapter 1 Test

2) 4x + 30 = 6x – 302x= 60x = 30

mRUS = 150, mRUT = 30

Linear Pairs RUT & RUS, RUS & SUV, RUT & TUV, TUV & SUV

Vertical Angles RUT & SUV, RUS & TUV

R

S

T

VU

4x + 30

6x - 30

Chapter 1 Test

3)

6 in

18 in

20 m

25 m

A = 108 in2

P = 48 in

A = 300 m2

P = 70 m

15 m

Chapter 1 Test

4) R -5

S -3

T -1

U 2

V 4

R S T U V

-5 -3 -1 2 4

A. AB bisects RV – False, RT = 4, TV = 5

B. S is the midpoint of RT – True, RS = 2, ST = 2

C. RT TV – False, RT = 4, TV = 5

D. The measures of RT + TV = 9, True, RT = 4, TV = 5, 4 + 5 = 9

A

B

Chapter 1 Test

5) A. Two planes never intersects at a point.

B. Four points are sometimes coplaner.

C. Obtuse angles are never less than ninety degrees in measure.

6) A. Collinear – two or more points on the same line

B. Between – for line A-B-C, B is between A and C

C. Linear Pair – two adjacent angles that in total equals 180 degrees

Chapter 1 Test

7)

A

B

C

D

The Angle Addition Postulate states that you can add adjacent anglestogether to determine the measure of the larger angle created.

mABC + mCBD = mABD

Chapter 1 Test

8)

2-2 Enrichment

2-2 Enrichment

2-2 Study Guide

2-2 Study Guide

2-2 Practice

2-2 Practice

2-2 Practice

Book work …

Page 766, Lessons 2-1 & 2-2

Lesson 2-1

Lesson 2-1

Lesson 2-1

Lesson 2-1

Lesson 2-2

Lesson 2-2

Lesson 2-2

Mini-Quiz to follow

Mini-Quiz

2-2 Deductive Reasoning

1) If the measure of an angle is greater than 90, then it is obtuse.

2) The measure of T is greater than 90.

3) Therefore, T is obtuse

2-2 Deductive Reasoning

1) If Julie works after school, then she works in a department store.

2) Julie works after school.

3) Julie works in a department store.

2-2 Deductive Reasoning

1) If William is reading, he is reading a magazine.

2) If William is reading a magazine, he is reading a magazine about computers.

3) If William is reading, then he is reading a magazine about computers.

2-2 Deductive Reasoning

1) If Henry studies his Geometry, then he passes the test.

2) If Henry passes the test, then he will get a good grade.

3) If Henry studies his Geometry, then he will get a good grade.

Proofs

Given:

Prove:

Statements Reasons

1) 1) Given

QED

Properties of Equality (p. 93)

Geometric Version (p. 93)

Essentials to a good proof

•State the theorem to be proved•List the given information•If possible, draw a diagram•State what is to be proven•Develop a system of deductive reasoning

Homework

2-3 Study Guide and Practice 2-3 Enrichment

More Theorems

Theorem 2 – 2 Supplement Theorem

If two angles form a linear pair, then they are supplementary angles.

Theorem 2 – 3

Congruence of angles is reflexive, symmetric, and transitive.

Theorem 2 – 4

Angles supplementary to the same angle or to congruent angles are congruent.

and even more Theorems

Theorem 2 – 5

Angles complementary to the same angle or to congruent angles are congruent.

Theorem 2 – 6

All right angles are congruent.

Theorem 2 – 7

Vertical angles are congruent.

Theorem 2 – 8

Perpendicular lines intersect to form four right angles.