Geometry

Today: Class Attendance /

Announcements Return / Review

Chapter 3 Tests 4.1 Notes / Break /

4.2 Notes Exit Slip Begin Homework

Be not afraid of going slowly; be afraid only of standing still.

Chinese Proverb

4.1/4.2 Triangles and Angles

Objectives:• Classify triangles• Find angle measures in a triangle • Identify congruent figures and corresponding

congruent parts• Prove triangles are congruent• Know 3 basic properties of triangles in a

triangle

Vocabulary: equilateral, isosceles, scalene, acute, equiangular, right, obtuse, interior angles, exterior angles

4.1 Classifying Triangles

Triangle:

Triangle Sum Theorem:

Triangle: 3 sided closed figure.

Triangle Sum Theorem: The sum of the measures of a triangle is 180º.

Examples: Find the measure of 1.

1. 2.

A

C

B

𝑚∠𝐴+𝑚∠𝐵+𝑚∠𝐶=180 ° Why?

4.2 Congruence and TrianglesTriangle Sum Theorem:The sum of the measures of a triangle is 180º.

Third Angle Theorem:If two angles in one triangle are congruent to two angles in another triangle, then the third angles are also congruent.

X

Y

Z

A

B

C

thenY, B and X A If Z. C

Use it in PROOF!!!

Given: MNO PQO

Prove: NMO QPO

N

QM

P

O

5 ESSENTIAL PARTS OF A PROOF.

1. List the given information.2. Identify conclusion to be proven.3. If possible, draw and mark a picture.4. Develop a system of reasoning.5. End with the idea to be proven.

Use it in PROOF!!!

Given: MNO PQO

Prove: NMO QPO

Statements Reasons

1) MNO PQO 1) Given2) MON POQ 2) Vertical Angles are Congruent3) NMO QPO 3) Third Angle Theorem

N

QM

P

O

Find the value of x:

D E

F

A

B

C

x.of value thefind E, B and DA If

87º

22º

(4x – 15)º

Use it with Algebra.

Break Time

Take a quick break. Get up, stretch out, talk to a neighbor, or try the following rebus puzzles…

Beaten black and blue

Middle C

Connections

Old Information:

Put it together:

Exterior Angle Theorem:The measure of an exterior angle of a triangle is equal to the sum of the measures the two nonadjacent interior angles.

1

2

3 4

Applying the Exterior Angle Theorem

Find the measure of 1.

1. 2.

Find the value of x.

x

72o (2x – 11)

Labeling Triangles

Vertex:

Adjacent Side:

Opposite Side:

Name the sides that are opposite and adjacent to each vertex.

Vertex: points joining the sides of the triangle.

Adjacent Side: sides sharing a common vertex.

Opposite Side: side opposite from the vertex.

Congruent Triangles

Congruent Figures:

Corresponding Sides:

Corresponding Angles:

Congruent Triangles:

A

B

C ED

F

Congruent Triangles also known as a congruency statement.

Classify by Angles

Right:

Classify ΔQRS

Obtuse:

Acute:

Equiangular:

36° 54°

Q

R

S

Right: contains one right angle.

Obtuse: contains one obtuse angle.

Acute: contains three acute angles.

Equiangular: contains three congruent angles. contains three 60° angles.

Classify By Sides

Equilateral:

Classify ΔABC

Isosceles:

Scalene:

A

B C

Equilateral: all sides congruent.

Isosceles: at least two sides congruent.

Scalene: no sides congruent.

Keep going…

Corollary to the Triangle Sum Theorem:The acute angles of right triangle are complementary.

Examples: Find the measure of 1.

1. 2.

A

CB

3-2-1 Exit Slip

Before you leave, complete the following exit slip. PUT SOME THOUGHT INTO THIS!

1. List 3 things you learned from today’s lesson.

2. List 2 concepts/ideas you thought were confusing.

3. List 1 thing you can do to understand the confusing/difficult concepts better.

Geometry

Assignment:4.1, 4.2 pgs.

198-200 #19-26, 31-39, 41-43, 47

Quiz 4.1-4.4 Friday

Be not afraid of going slowly; be afraid only of standing still.

Chinese Proverb