Think: Vertical or linear pair? Set up equation and solve for x, justifying each step 1) Place...

Think: Vertical or linear pair? Set up equation and

solve for x, justifying each step

2 5x

1) Place binder and text on your desk.2) Place everythingeverything from RIGHT side of folders into correct section of your binder.3) Warm-up (TOP front)

4 11x

Honors Geometry 1 Oct 2012

objectiveStudents will recognize and find missing angle measures.TUTORING:TUTORING:Monday 3 – 3:45Monday 3 – 3:45Thursday 1:30 – 2:15Thursday 1:30 – 2:15HOMEWORK due Tuesday: HOMEWORK due Tuesday: pg. 131: 1- 6, 9, 14 – 16 (sketches, K’s, W’s, explain!)pg. 131: 1- 6, 9, 14 – 16 (sketches, K’s, W’s, explain!)

words to know- add to vocabinductive observing data, recognizing patterns,reasoning then making a generalization

conjecture the generalization; “if…then….”

examples?

converse switch the “if….then…” parts ex. if two angles are vertical angles, then they are congruent

converse would be (which is not true) if two angles are congruent, then they are vertical angles

transversal a line intersecting 2 or more lines

angles formed by a transversal intersecting 2 lines:corresponding same relative positionangles (CA)

alternate inside the two lines on oppositeinterior side of transversalangles (AIA)

alternate outside the two lines on opposite side ofexterior transversalangles (AEA)

TRANSVERSALTRANSVERSAL

corresponding angles (CA)

1 and 5 2 and 63 and 7 4 and 8

alternate interior angles (AIA)

3 and 6 4 and 5

alternate exterior angles (AEA)

2 and 7 1 and 8

In your vocabulary notes,sketch the figure and identify:

transversalcorresponding angles (CA)corresponding angles (CA)alternate interior angles alternate interior angles (AIA)(AIA)alternate exterior angles alternate exterior angles (AEA)(AEA)

section 2.6 Investigationswhat if the two lines ARE parallel?

Investigation 1- steps 1 and 2- whole classNOTE– “paper” = notebook paper “patty paper” = “patty paper”

compare your results with your group so what do you think?

Verbally discuss the three conjectures (CA, AIA and AEA) on page 129 with your group

what about the converse?

Investigation 2- pg. 130 “paper” = notebook paper “patty paper” = “patty paper”

whole class

3 conjectures:1.1.Linear pairs add up to 180Linear pairs add up to 18000 2.2.Vertical angles are congruentVertical angles are congruent

3. If two 3. If two parallelparallel lines are cut by lines are cut by a a transversal, then transversal, then corresponding corresponding anglesangles (CA)are CONGRUENT (CA)are CONGRUENT, , alternate interior anglesalternate interior angles (AIA)are CONGRUENT (AIA)are CONGRUENT and and alternate exterior anglesalternate exterior angles (AEA)are CONGRUENT.(AEA)are CONGRUENT.NOTE- this is true ONLY when NOTE- this is true ONLY when transversal cuts transversal cuts PARALLELPARALLEL lines!!lines!!

1 2

12

12

1 2

1

2

converse of IfIf 2 lines are cut by a transversalparallel lines to form congruent pairs ofconjecture CA, AIA and AEA, thenthen the lines are parallel.are parallel.

NOTE proof format for “angle chases”

• see handout• Use for all angle chases1) start with identifying the given angles on your

diagram2) first steps for proof are writing what is given3) follow handout!

finish

ALL students must complete- if not completed in class, FINISH for HOMEWORK- due Friday! (there will be other homework assigned)1) Angle Pair Relationship Worksheet2) 2.5 Angles Worksheet3) 2.6 Handout

Be ready to share your results with the class

debrief

what have you learned?

what is easy?

what might be confusing to some students?