Geom.–Ch.1.3AnglesMr.Deyo

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Bytheendoftheperiod,studentswillapplytheangleadditionpostulateandanalyzecongruentangles.

Theywilldemonstratethisbycompletingagraphicorganizerandsolvinganglemeasurementproblemsinapairactivity.

Learning Target

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.  How are the two pictures similar? 2.  How are they different? 3.  How can these two pictures be related to math?

1) Angle2) Acute3)  Right4) Obtuse

Vocabulary

1.  Teachersaystheword.•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

DAY 3 and/or DAY 4 1. Review the word

♦ Friendly Definition ♦ Physical Representation

2. Show how the word works ♦ Synonyms/antonym ♦ Word Problems ♦ Related words/phrases ♦ Example/non-example

Friendly Definition Sketch

Wordwork Sentence

DAY 2 1. Review word

♦ Friendly Definition ♦ Physical Representation

2. Draw a sketch

DAY 5 1. Review the word

♦ Friendly definition ♦ Physical Representation

3. Write a sentence  at least 2 rich words (1 action)  correct spelling  correct punctuation  correct subject/predicate agreement  clear and clean writing

DAY 1 1.  Use Visuals

2.  Introduce the word ♦ Friendly Definition ♦ Physical Representation

3.  Use Cognates

4.  Write friendly definition

5.  Physical Representation

WordList1.  2.  3.  4. 

Notes:An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

NaminganAngle

Vertex: ∠3Letters: ∠ _________

∠ _________Number:

∠

Notes: The measure of an angle is usually given in degrees.

A. m∠YXZ B. m∠ZXW C. m∠WXV

D. m∠YXV

Notes:

_______+_______=________

A‐BProblemAnotes:

m∠DEG = 115°, and m∠DEF = 48°. Find m∠FEG

m∠_____+m∠_____=m∠ ___

_____+_____=______

A‐BProblemACheck:

m∠DEG = 115°, and m∠DEF = 48°. Find m∠FEG

m∠DEG = m∠DEF + m∠FEG 115° = 48° + m∠FEG

67° = m∠FEG

∠ Add. Post. Substitute the given values. Subtract 48 from both sides.

Simplify.

–48° –48°

A‐BProblemBSOLVE!!

m∠XWZ = 121°, m∠XWY = 59°. Find m∠YWZ.

A‐BProblemBCheck!!

m∠XWZ = 121°, m∠XWY = 59°. Find m∠YWZ.

m∠YWZ = m∠XWZ – m∠XWY

m∠YWZ= 121° – 59°

m∠YWZ= 62°

∠ Add. Post.

Substitute the given values.

Subtract.

StormCheck(Think,Write,Discuss,Report)

1)  SummarizetheAngleAdditionPostulateinyourownwords?

2) HowisitsimilartotheSegmentAdditionPostulate?

1)_____________________________________

_______________________________________.

2)  ____________________________________.

Learning Target

Bytheendoftheperiod,studentswillapplytheangleadditionpostulateandanalyzecongruentangles.

Theywilldemonstratethisbycompletingagraphicorganizerandsolvinganglemeasurementproblemsinapairactivity.

Notes:Congruent angles are angles that have the same measure. In the diagram, m∠ABC = m∠DEF, so you can write ∠ABC ≅ ∠DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.

Notes:An angle bisector is a ray that divides an angle into two

congruent angles. JK bisects ∠LJM; thus ∠LJK ≅ ∠KJM.

m∠_____+m∠_____=m∠ ___

____+____=____

m∠ ___=m∠___

___=___

A‐BProblemAnotes:

KM bisects ∠JKL, m∠JKM = (4x + 6)°, and m∠MKL = (7x – 12)°. Find m∠JKM.

A‐BProblemACheck:Step 1 Find x.

m∠JKM = m∠MKL

(4x + 6)° = (7x – 12)° +12 +12

4x + 18 = 7x –4x –4x

18 = 3x 6 = x

Def. of ∠ bisector

Substitute the given values. Add 12 to both sides.

Simplify.

Subtract 4x from both sides. Divide both sides by 3. Simplify.

Step 2 Find m∠JKM. m∠JKM = 4x + 6

= 4(6) + 6

= 30°

Substitute 6 for x.

Simplify.

A‐BProblemBSOLVE!!

KM bisects ∠JKL, m∠JKM = (2x + 3)°, and m∠MKL = (7x – 12)°. Find m∠JKM.

A‐BProblemBCheck:Step 1 Find x.

m∠JKM = m∠MKL

(2x + 3)° = (7x – 12)° +12 +12

2x + 15 = 7x –2x –2x

15 = 5x 3 = x

Def. of ∠ bisector

Substitute the given values. Add 12 to both sides.

Simplify.

Subtract 4x from both sides. Divide both sides by 3. Simplify.

Step 2 Find m∠JKM. m∠JKM = 2x + 3

= 2(5) + 3

= 13°

Substitute 6 for x.

Simplify.

StormCheck(Think,Write,Discuss,Report)

1) Whatdoesananglebisectordo?2) Howdoesananglebisectorhelpmesolvefor

anglemeasures?

1)Ananglebisector_____________________

_______________________________________. 2)Ananglebisectorhelpsmesolveforangle

measuresby____________________________

_______________________________________.

Vocabulary Review

1.  Teachersaystheword.•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

1) Angle2) Acute3)  Right4) Obtuse

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Learning Target

Bytheendoftheperiod,studentswillapplytheangleadditionpostulateandanalyzecongruentangles.

Theywilldemonstratethisbycompletingagraphicorganizerandsolvinganglemeasurementproblemsinapairactivity.

Ticket OUT.

Classify each angle as acute, right, or obtuse.

1. ∠WTU ___________

2. ∠XTS ___________

3. ∠XTU ___________

*4) ∠STU ___________