Do Now• I need a volunteer for the class job of pass-out

specialist (benefit, you get a pass on Do Nows for the week)

1. Find the measure of angle b

2. Find the value of x.

Review

• Name the angle types and solve for b in each angle.

Intro to Triangles

Students will find measures of angles in triangles.

Video

• http://www.youtube.com/watch?v=vw-rOqDBAvs&feature=related

Triangle Sum Theorem

• Triangle Sum Theorem – the sum of the measures of the angles of a triangle is 180.

Example #1

• What is the measure of angle 1?

Example #1

• What is the measure of angle 1?

• <1 = 180 – 37 – 57 = 86

How many Triangles?

How many Triangles?

Answer: 3! ABD, BDC, and the big triangle ABC.

How many triangles?

Example #2• Find the values of x, y, and z.

Example #2• Find the values of x, y, and z.

• 43 + 59 + x = 180. x = 180 – 59 – 43. x = 78• x + y = 180. 78 + y = 180. y = 180 – 78. y = 102• y + z + 49 = 180. 102 + z + 49 = 180. z = 180-49-102. z = 29.

Exterior Angle of a Polygon

• Exterior Angle of a Polygon – an angle formed by a side and an extension of an adjacent side.– 1

• Remote Interior Angles – the two nonadjacent interior angles– 2 and 3

• Name the exterior angle of the polygon and the remote interior angles in the diagram below.

Triangle Exterior Angle Theorem

• The measure of each exterior angle of a triangle equals the sum of its two remote interior angles.

Example #1

• What is the measure of angle 1?

Example #1

• What is the measure of angle 1?

• <1 = 80 + 18• <1 = 98

Example #2

• What is the measure of angle 2?

Example #2

• What is the measure of angle 2?

• <2 + 59 = 124• <2 = 124 – 59• <2 = 65

You Try

• On the back of your notes!• Find the values of the variables x, y, and z.

You Try

• Find the values of the variables x, y, and z.

• y = 36, z = 90, x = 38

You Try

On the back of your notes: Find the values of the variables and the measures of the angles.

You Try

On the back of your notes: Find the values of the variables and the measures of the angles.

• (2x + 4) + (2x – 9) + x = 180• x = 37

Exit Ticket

1. Find the value of <1 in the diagram to the right

2. Find the value of x, y, and z

3. Solve for x.

HOMEWORK!!!: Page 75 1,3,4,8,10,17,18

Do Now

1. Find

2. Find

Exit Ticket 10/1

1. Find the value of <1 in the diagram to the right

2. Find the value of x, y, and z

3. Solve for x.

HOMEWORK!!!: Page 75 1,3,4,8,10,17,18

Congruent Figures

Students will be able to find corresponding parts of congruent

figures

Congruent Figures

• Congruent figures have the same size and shape.

Congruent Figures

• Congruent Polygons have congruent corresponding parts - their sides and angles match!!

Congruent Figures

• ***When naming congruent polygons, you MUST list the corresponding vertices in the SAME ORDER.

Video

• http://app.discoveryeducation.com/player/view/assetGuid/A39E2AC4-E031-4E6A-8115-FC59EF04BF76

Let’s Practice!• WXYZ JKLM

1. Line segment WX _?_2. Line segment KL _?_3. Line segment MJ _?_4. _?_5. _?_6. _?_

Let’s Practice

1. Complete the following statements: Given: ΔNMK ΔVYZ

a) line segment line segment _?_ b) line segment line segment _?_ c) _?_ d) _?_

Let’s Practice!

Third Angles Theorem

You try!

• What is

You try

• , 72. What is ? (Draw a diagram to help you answer the question. Think back to the last problem)

Exit Ticket 10/2

1. Complete the following statements: Given: ΔDEF ΔGZT a) line segment line segment _?_ b) _?_

2. ∆ABC ∆LMN. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.)

3. , . What is ? (Draw a diagram to help you answer the question.)

Do Now1. Complete the following statements: Given: ΔSML

ΔTNYa) line segment line segment _?_ b) _?_

2. ∆QRS ∆TUV. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.)

3. , . What is ? (Draw a diagram to help you answer the question.)

Exit Ticket 10/2

1. Complete the following statements: Given: ΔDEF ΔGZT a) line segment line segment _?_ b) _?_

2. ∆ABC ∆LMN. Name all of the pairs of corresponding congruent parts. (Draw a picture of the two triangles on a separate sheet of paper to help you answer the question.)

3. , . What is ? (Draw a diagram to help you answer the question.)

Yesterday we learned that…

• … two polygons were congruent if all sides AND all angles were congruent.

• But that’s WAY more info than we need!!

Today we will learn…

• …how to prove that two triangles are congruent by using:1. 3 pairs of corresponding sides2. 2 pairs of corresponding sides and 1 pair of

corresponding angles3. 1 pair of corresponding sides and 2 pairs of

corresponding angles

Tick Marks and Curves

What do those red tick marks and curves mean?

You Try!1. The single tick mark means line segment

NJ _?_2. The double tick marks mean FR _?_ 3. The curve means _?_

Side-Side-Side Postulate (SSS)

Side-Angle-Side Postulate (SAS)

Identifying Congruent TrianglesLook at the triangles: 1. How many congruent sides do we have (count the

sets of tick marks). 2. How many congruent angles do we have ? 3. Are the angles between the sides?4. Are the triangles congruent? Justify.

Identifying Congruent TrianglesLook at the triangles: 1. How many congruent sides do we have (count the

sets of tick marks). 2. How many congruent angles do we have ? 3. Are the angles between the sides?4. Are the triangles congruent? Justify.

Identifying Congruent Triangles

Would you use SSS or SAS to prove the triangles congruent? If there is not enough information, write not enough information.

Identifying Triangles with Funky Shapes

Are the following triangles congruent? Justify.

What else do I need to know?

What other information do you need to prove ABC ADC by SAS? Explain your answer.

What else do I need to know?What other information do you need to prove by SAS? Explain your answer.1. What does SAS mean? 2. What do I have currently?3. What else do I need?

What else do I need to know?What other information do you need to prove ABC ADC by SAS? Explain your answer.1. Answer: NH DR2. Explanation: Already know JH FR and so with NH

DR, we have a side, and angle in between and another side.

You Try

What other information do you need to proveABC ADC by SSS? Explain your answer.

Exit Ticket

1. Are the triangles to the right congruent? Justify.

2. What other information do you need to prove

Do Now

1. Are the triangles at the right congruent? Justify

2. Are the triangles at the right congruent? Justify

3. What are the two postulates we learned yesterday to prove two triangles are congruent?

Exit Ticket from Yesterday

1. Are the triangles to the right congruent? Justify.

2. What other information do you need to prove

Two more postulates

Angle-Side-Angle Postulate (ASA)

Angle-Angle-Side Theorem (AAS)

All Together Now• 4 Ways to prove triangles congruent:

1. SSS – If two triangles have THREE congruent pairs of sides, they are congruent by SSS

2. SAS – If two triangles have TWO congruent pairs of sides and an angle BETWEEN them, they are congruent by SAS

3. ASA – If two triangles have TWO congruent pairs of ANGLES and a side BETWEEN them, they are congruent by ASA

4. AAS – If two triangles have TWO congruent pairs of ANGLES and a side NOT BETWEEN them, they are congruent by AAS.

Which two triangles are congruent by ASA?

• List the theorem/postulate that you would use to prove the two triangles are congruent. If none apply, write not enough information.

1.

3.

2.

4.

Exit Ticket

Do Now

Let’s Finish our Worksheets

• You will be turning in ASA and AAS today!• SSS and SAS will be due at the beginning of

class Monday.

Worksheet• Find EVERY vertical angle (“kissing Vs”) and

shared side and draw in angle marks or tick marks

• Label EVERY angle with an A and side with an S

Worksheet• Find EVERY vertical angle (“kissing Vs”) and

shared side and draw in angle marks or tick marks

• Label EVERY angle with an A and side with an S

Worksheet Back Page

• You should have labeled all given angles and sides

Worksheet Back Page• You should have labeled all given angles and

sides• NOW find the angle or side that will prove

congruence by the theorem listed

Worksheet Back Page• Finally, YOU MUST LIST THE NEW INFORMATION

(NEW SIDES/ANGLES)• You will NOT receive credit unless you do this

∠𝑉𝐻𝐺≌∠𝐼𝐺𝐻

∠𝐹𝐾𝐿≌∠ 𝐽𝐿𝐾

Practice

Justification:

CA

Practice

Practice

• List the theorem/postulate that you would use to prove the two triangles are congruent. If none apply, write not enough information.

1.

3.

2.

4.