1/4 Monday- Intro to Rotations, Reflections, Translations (ppt) 1/5 Tuesday- Kaleidoscope Activity (pdf) 1/6 Wednesday- Congruence ppt 1/7 Thursday- Dilations 1/8 Friday- Dilations and 15 min activity 1/11 Monday- Conferences 1/12 Tuesday- Conferences 1/13 Wednesday- Dilations 1/14 Thursday- Similarity 1/15 Friday- Review of Transformations 1/19 Tuesday- Work on portfolios 1/20 Wednesday- Midterms 1/21 Thursday- Midterms 1/22 Friday- Midterms 1/26 Tuesday- Interior and Exterior Angles 1/27 Wednesday- Interior and Exterior Angles 1/28 Thursday- Supplementary Angles 1/29 Friday- Complimentary Angles, Vertical Angles, and Adjacent Angles Agenda

Bell Ringer What is the only difference between SIMILAR and CONGRUENT shapes?

AnglesAngles MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.) MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.)

Learning Scale for Angles: Level 1  I can recall vocabulary such as: Angle, angle sum, angle- angle criterion, argument, exterior angle, fact, line, parallel, similarity, triangle  I can recall facts about angle sum and exterior angles of triangles, and the angle-angle criterion for similarity of triangles.  I can recall vocabulary such as: Angle, angle sum, angle- angle criterion, argument, exterior angle, fact, line, parallel, similarity, triangle  I can recall facts about angle sum and exterior angles of triangles, and the angle-angle criterion for similarity of triangles.

Class Discussion: Now that you know that, what do you think about this? What is the ONLY thing that is different in SIMILAR shapes? …their size! So, are similar shapes angles the same or different?

What do you call a 3-sided polygon? A triangle! (This means that the shape has three sides AND three angles…)

Interior Angles of a Polygon The interior angles of a polygon are the angles inside the polygon, formed by two adjacent sides. (Adjacent means “next to”) When all the interior angles are added together in a triangle it should equal 180 degrees! For example, ∆ABC (read as “triangle ABC”) has interior angles:  ABC,  BAC,  BCA The interior angles of a polygon are the angles inside the polygon, formed by two adjacent sides. (Adjacent means “next to”) When all the interior angles are added together in a triangle it should equal 180 degrees! For example, ∆ABC (read as “triangle ABC”) has interior angles:  ABC,  BAC,  BCA This symbol means “angle”

Key Information!!!! The interior measures of a triangle add up to 180° The measures of angles A, B, and C all add up to 180. The interior measures of a triangle add up to 180° The measures of angles A, B, and C all add up to 180.

Reviewing the Different Types of Triangles Equilateral: All sides and angles equal (so all angles are 60°). Isosceles: Two sides and two angles are equal. Scalene: All the side lengths and angles are different. Acute: All angles are less than 90°. Right: One angle is 90° shown by a square in that corner. Obtuse: One angle is more than 90°.

Whiteboards! (NO CALCULATORS!!) Find the missing angle, C.

Whiteboards!

Hint: notice that two of the angles are both labeled “B”. So do you think these angles will be different measures or the same measures?

Exterior Angles of a Polygon An exterior angle of a polygon is an angle that forms a linear pair with an interior angle. It is an angle outside the polygon formed by one side and one extended side of the polygon. Copy down the Picture! Example: ∆ABC has exterior angle:  ACD. It forms a linear pair with interior  ACB. An exterior angle of a polygon is an angle that forms a linear pair with an interior angle. It is an angle outside the polygon formed by one side and one extended side of the polygon. Copy down the Picture! Example: ∆ABC has exterior angle:  ACD. It forms a linear pair with interior  ACB. A B C D Exterior: Outside triangle Interior: Inside Triangle

Supplementary Angles Two Angles are Supplementary when they add up to 180 degrees. The two angles below (140° and 40°) are Supplementary Angles because they add up to 180°: Notice that together they make a straight line or a straight angle. Two Angles are Supplementary when they add up to 180 degrees. The two angles below (140° and 40°) are Supplementary Angles because they add up to 180°: Notice that together they make a straight line or a straight angle. interiorexterior

Whiteboards! A ° B ° C ° D °

Whiteboards! Step 1: Find out what the missing interior angle is. Step 2: Recall that the missing interior and m  1 are supplementary angles! So they should add up to 180.

Whiteboards!

Exit Ticket Tuesday, January 26, 2016  Tell me the difference between interior and exterior angles.  How many degrees does a triangle have?  How many degrees does a straight line have?  Tell me the difference between interior and exterior angles.  How many degrees does a triangle have?  How many degrees does a straight line have?

Homework : Vocabulary Maps Vocabulary Words: 1. Interior Angle 2. Exterior Angle 3. Triangle (include the sum of it’s angles in the definition) 4. Supplementary Angles 5. Complimentary Angles 6. Similar 7. Congruent PictureDefinition Example Problem with Answer Sentence Word

Extra Credit Opportunity!  For 20 extra credit points go to my website, click on the Pre-Algebra Assignments page and complete the assignment “Interior and Exterior Angles Extra Practice”

Bell Ringer Friday January 29 th 1. Pull out your Vocab Maps I’m coming around to check them! 2. Name the three interior angles of triangle C. 3. Name the straight angle. (Note: when naming angles, you ALWAYS name three letters)

AnglesAngles MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.) MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.)

Learning Scale for Angles: Level 1  I can recall vocabulary such as: Angle, angle sum, angle- angle criterion, argument, exterior angle, fact, line, parallel, similarity, triangle. transversal  I can recall facts about angle sum and exterior angles of triangles, and the angle-angle criterion for similarity of triangles.  Identify angles created when a parallel line is cut by a transversal  I can recall vocabulary such as: Angle, angle sum, angle- angle criterion, argument, exterior angle, fact, line, parallel, similarity, triangle. transversal  I can recall facts about angle sum and exterior angles of triangles, and the angle-angle criterion for similarity of triangles.  Identify angles created when a parallel line is cut by a transversal

TIME TO TAKE NOTES!!!

Complementary and Supplementary Angles Complementary Angles Two angles whose measures add up to 90 degrees Supplementary Angles Two angles whose measures add up to 180 degrees. Supplementary angles can be placed to form a straight line.

Vertical and Adjacent Angles Vertical Angles Two angles formed by intersecting lines. They cannot be adjacent (next to each other) but are always equal in degree measure. They are across from one another in the corners of the "X" formed by the lines Adjacent Angles Angles that are simply next to each other. They share a common side and a common point (vertex). They don’t have to add up to a specific degree amount.

Parallel Lines and Transversals When parallel lines get crossed by another line (called a transversal), you can see that many angles are the same, as in this example:

YOU HAVE 25 MINUTES!!!!! We are going to have a scavenger hunt! I will pass out a tracking worksheet to each pair (so you are working in two’s). You will notice that there are vegetables and answers posted around the room (and maybe even in the pod!) Start at any poster. Read the problem at the bottom, work it out, and then find that answer at the top of another poster. Write down the vegetable shown and then work out the problem at the bottom of that poster. Continue this trend. You have 12 posters to work through! You may use a calculator. We are going to have a scavenger hunt! I will pass out a tracking worksheet to each pair (so you are working in two’s). You will notice that there are vegetables and answers posted around the room (and maybe even in the pod!) Start at any poster. Read the problem at the bottom, work it out, and then find that answer at the top of another poster. Write down the vegetable shown and then work out the problem at the bottom of that poster. Continue this trend. You have 12 posters to work through! You may use a calculator.

Homework Friday January 29 th Angles and Relationships Homework Sheet

Bell Ringer Monday In the diagram below, lines m and n are parallel. If ∠ 1 is 120°, what do you think could be the measure of ∠ 2?

AnglesAngles MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.) MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.)

Scale for Angles

Vertical, Corresponding, Alternate Interior, Alternate Exterior, and Consecutive Interior Angles Vertical Angles:  a,  d and  b,  c and  e,  h and  f,  g Corresponding Angles:  a,  e and  c,  g and  b,  f and  d,  h Alternate Interior:  c,  f and  d,  e Alternate Exterior:  a,  h and  b,  g Consecutive Interior:  c,  e and  d,  f Vertical Angles:  a,  d and  b,  c and  e,  h and  f,  g Corresponding Angles:  a,  e and  c,  g and  b,  f and  d,  h Alternate Interior:  c,  f and  d,  e Alternate Exterior:  a,  h and  b,  g Consecutive Interior:  c,  e and  d,  f

In your notes, figure this out: Hints: 1. Remember what vertical angles are. 2. A triangle has 180 °. 3. Supplemental angles also add up to 180 °.

In your notes, figure this out: Hints: 1.Remember what vertical angles are. 2.Recall what corresponding angles are. 3.A square in a triangle’s corner means 90 °. 4.A triangle has 180 °.

Practice with Angles Grab a whiteboard, marker, and fabric square! We are going to go through some practice problems on mathisfun.com Grab a whiteboard, marker, and fabric square! We are going to go through some practice problems on mathisfun.com ometry/parallel-lines.html

TIME TO AMP UP THE LEARNING! I AM GOING TO PASS OUT THREE TASKS…WHATEVER WE DO NOT FINISH AS A CLASS WILL BE HOMEWORK!

Homework Finish worksheet if we did not finish together in class.

Bell Ringer Friday, January 29, Turn your homework in to my polka dot box. 2. Take out a separate sheet of paper. I will stamp your homework and then we will be going over it with my doc cam.

AnglesAngles MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.) MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.  Define similar triangles.  Define and identify transversals.  Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)  Justify that the sum of interior angles equals 180.  Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.  Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.)

Scale for Angles

Today, we will be looking at: Angle Theory and Practice FSA Questions Grab a ruler from the back table. On your blank sheet of paper, draw two right triangles. They will be different sizes. Triangle A will have a leg of 3 inches and a leg of 4 inches. (The hypotenuse—the long side—should end up measuring 5 inches.) Triangle B will be similar to Triangle A, but dilated by a scale factor of 1.5 (so all the side lengths should be 1.5 times longer than Triangle A’s)…grab a calculator if you need one. ClassworkClasswork

Questions to ask yourself… Q: Are your two triangles similar? A: Yes, the triangles are similar. The theorem on similar triangles states that when we have two triangles △ and △ ′′′ with corresponding angles that are equal and corresponding side lengths that are proportional, then the triangles are similar. Q: Why is it that you only need to construct triangles where two pairs of angles are equal but not three? A: If we are given the measure of two angles of a triangle, then we also know the third measure because of the triangle sum theorem. All three angles must add to °, so showing two pairs of angles are equal in measure is just like showing all three pairs of angles are equal in measure. Q: Do you think that what you observed will be true when you construct a pair of triangles with two pairs of equal angles? Explain. Q: Are your two triangles similar? A: Yes, the triangles are similar. The theorem on similar triangles states that when we have two triangles △ and △ ′′′ with corresponding angles that are equal and corresponding side lengths that are proportional, then the triangles are similar. Q: Why is it that you only need to construct triangles where two pairs of angles are equal but not three? A: If we are given the measure of two angles of a triangle, then we also know the third measure because of the triangle sum theorem. All three angles must add to °, so showing two pairs of angles are equal in measure is just like showing all three pairs of angles are equal in measure. Q: Do you think that what you observed will be true when you construct a pair of triangles with two pairs of equal angles? Explain.

Theorem for AA Criterion (Angle-Angle Criterion) Two triangles with two pairs of equal corresponding angles are similar. (This is known as the AA criterion for similarity.) When two pairs of corresponding angles of two triangles are equal, the triangles are similar. Two triangles with two pairs of equal corresponding angles are similar. (This is known as the AA criterion for similarity.) When two pairs of corresponding angles of two triangles are equal, the triangles are similar.

Are these triangles similar? The triangles are NOT similar because they have just one pair of corresponding equal angles. By the triangle sum theorem, ∠ = ° and ∠ = °. Since similar triangles must have equal corresponding angles, we can conclude that the triangles shown are not similar.

The triangles shown below are similar. Use what you know about similar triangles to find the missing side lengths and. Look at where the angles correspond. What does 12 correspond with? What does 16.5 correspond with? What does y correspond with? Look at where the angles correspond. What does 12 correspond with? What does 16.5 correspond with? What does y correspond with?

FSA Sample Question An architect is using isosceles triangles in the design of a bridge. In the diagram below, all line segments represent the steel beams needed to build this section of the bridge. Triangle DEC is similar to ΔCAB and congruent to ΔAFG. What is the length, in feet (ft), of segment EC ? An architect is using isosceles triangles in the design of a bridge. In the diagram below, all line segments represent the steel beams needed to build this section of the bridge. Triangle DEC is similar to ΔCAB and congruent to ΔAFG. What is the length, in feet (ft), of segment EC ?

FSA Sample Question A. 45° B. 35° C. 25° D. 15° A. 45° B. 35° C. 25° D. 15°

HOMEWORK Friday, January 29, 2016