Mr. Ohashi's Math 8 Website

Eighth Grade Math at Eckstein Middle School

Tag Archives: geometry

Friday, 6/16: Geometry Quiz (Day 14 of 14)

Learning Target: Quiz!
Handouts: None!

We had a quiz today! There is no homework! Don’t forget that the last day to turn in late/missing work is Monday of next week! Have a great weekend!

Thursday, 6/15: Geometry Quiz Review (Day 13 of 14)

Learning Target: Review geometry concepts in order to get ready for the quiz.
Handouts: Geometry Quiz Review (Turn in: Fri, 6/16)

We have our last quiz of the year tomorrow! For the quiz, you should be able to:

  • Identify and name angle relationships using geometry vocabulary.
  • Use angle relationships to find the measures of unknown angles.
  • Use the interior angle sum formula.
  • Find the measure of one interior angle of a regular polygon.
  • Set up and solve algebra equations to find unknown angle measures.

 
Your homework is to finish up the Quiz Review. Also, the last day to turn in late/missing work is Monday of next week!

Wednesday, 6/14: Mixed Geometry Review (Day 12 of 14)

Learning Target: Use angle relationships to determine unknown angle measures.
Handouts: Mixed Geometry Review (Turn in: Thurs, 6/15)

Today we had a mixed review of all the geometry work that we have been doing! I even did #1 and #2 with you on the overhead!

Third & fifth periods should finish #1-12. Fourth period should finish #1-13. Don’t forget that we have a quiz on Friday!

Tuesday, 6/13: Equal Angles (Day 11 of 14)

Learning Target: Use angle relationships to determine unknown angle measures.
Handouts: Equal Angles (Turn in: Wed, 6/14)

Today we learned a few new symbols. The symbols drawn on the angles below show that the angles are equal in measure. Notice that in the parallelogram, one pair of angles is equal, but not equal to the other pair of angles.

If you have a regular polygon, all side lengths are equal and all angles are equal (like the pentagon below). We can actually find the measure of each of the interior angles using the interior angle sum formula. Since all of the angles are equal, divide the interior angle sum by the number of angles!

Third period should finish #1-8. Fourth & fifth period should finish #1-6. Don’t forget that we have a quiz on Friday!

Monday, 6/12: Using Interior Angle Sums (Day 10 of 14)

Learning Target: Use the interior angle sum formula to find unknown angle measures.
Handouts: Using Interior Angle Sums (Turn in: Tues, 6/13)

Today we used the interior angle sum formula that we came up with last week. For example, if we know how many sides a polygon has, we can determine the interior angle sum (see the first example below). But today we also had to apply the formula to solve problems. In the second example below, we know the interior angle sum of a polygon, but we want to know how many sides it must have. We can set up and solve an algebra equation using the formula.

Almost every single problem on today’s assignment needed the interior angle sum formula in some way! Your homework is to finish #1-13. Also, we have a quiz on Friday!

Friday, 6/9: Class Expectations Posters

Learning Target: Make posters to review the class expectations.
Handouts: None

All year, you have been seeing the class expectations posters that last year’s students made. Today, you got a chance to make one with your table group. Remember, the best of the best will be put up on the wall for next year’s students to look at every day!

There is no homework. Have a great weekend!

Thursday, 6/8: Interior Angle Sums (Day 9 of 14)

Learning Target: Explore polygons to find a formula for the interior angle sum of any polygon.
Handouts: Interior Angle Sums (Turn in: Fri, 6/9)

Today we explored the interior angles of polygons. We know that the interior angles of any triangle always add up to 180 degrees. This is called an interior angle sum… because it is all of the interior angles added together (the sum!). Using our knowledge of triangles, we can then find the interior angle sum of any polygon by cutting the polygon up into triangles! To find the interior angle sums, pick a vertex (corner) and draw lines to other corners to form triangles. Since each triangle has 180 degrees in it, the interior angle sum of the polygon will be the number of triangles times 180 degrees.

We did the first part of the assignment together and found that there is a formula for finding this information without cutting up the shapes! If we take the number of sides of subtract 2, we know how many triangles are in the polygon. Then we can multiply that number of 180 to find the interior angle sum! We wrote that formula in our notes:

Your homework is to finish #1-5.

Wednesday, 6/7: Showing Your Work in Geometry (Day 8 of 14)

Learning Target: Use geometry vocabulary to identify and justify angle measures.
Handouts: Finding Angle Measures (Turn in: Thurs, 6/8)

We had more work with the types of geometry problems that we have been doing – completing tables to justify angle measures, setting up algebra equations to solve for unknown angle measures, and determining if triangles are similar.

Your homework is to finish #1-7. We will add some new geometry properties tomorrow!

Tuesday, 6/6: Showing Your Work in Geometry (Day 7 of 14)

Learning Target: Use geometry vocabulary to identify and justify angle measures.
Handouts: Showing Your Work (Turn in: Wed, 6/7)

Today we continued our work finding angle measures using angle relationships, but today you also had to justify your answers! This is what showing your work looks like in geometry. To do this, you complete a two column chart. The first column is titled “Statements” and is where you write the angle measures that you find. The second column is titled “Reasons” and is where you write how you know the angle measure using geometry vocabulary. Here is an example…

I would like you to fill in each line of the table as you find each angle. Do NOT fill in the diagram first and then complete the table because you won’t remember how you found each angle! Find the angle in the diagram, then fill in the line in the table, so that you will be able to correctly state how you know! Also, make sure you write each angle measure into the diagram so that it is easier to find the next angle measure!

Notice a couple of things up above… When we give the angle measures, we include the m before the angle. When we are referring to angles (on the Reasons side), we do not need the m. Also, we list the angles that we find in the order that we find them. This allows a person reading the table to clearly see how the problem was solved. Be sure to include the angles that you are referring to in the reasons column. Don’t just write down “supplementary angles”, state which two angles are supplementary! And finally, notice how I filled in the diagram with the angles.

I would like you to finish #1-6 for the classwork. This is no additional homework!

Monday, 6/5: Algebra and Geometry (Day 6 of 14)

Learning Target: Use algebra to solve geometry problems.
Handouts: Algebra & Geometry (Turn in: Tues, 6/6)

Today’s focus was on using algebra to solve geometry problems. For each diagram, you had to set up an algebra equation based on the angle relationships. Once you solve it, you then need to go back and calculate the measure of the unknown angles.

Your homework is to finish #1-6.

Friday, 6/2: Angle Relationships (Day 5 of 14)

Learning Target: Use angle relationships to identify angle measures.
Handouts: More with Angle Relationships (Turn in: Mon, 6/5)

We started today by writing down the rule for triangle similarity. We know that if two angles of one triangle match two angles of another triangle, then the third angles must also match and the two triangles must be similar!

Yesterday, we looked at the pattern of angles formed when parallel lines are intersected by another line. There are names for each of these angle relationships! Today, we completed the back page of our notes that have all of the angle relationships in pictures!

If you’d like to see a video describing these relationships, check it out here:

We also had some problems where a triangle was intersected by a line that was parallel to one of its sides. We found that this always creates a similar smaller triangle!

In class, you had to complete #1-6. There is no additional homework, so have a great weekend!

Thursday, 6/1: Parallel Lines and Angles (Day 4 of 14)

Learning Target: Explore parallel lines in order to discover more angle relationships.
Handouts: Angles & Parallel Lines (Turn in: Fri, 6/2)

Today we learned some more angle relationships. When two lines intersect, the angles across from each are equal. Those angles are called vertical angles.

We also looked at the angles that are formed when parallel lines are intersected by another line (a transversal). This forms eight angles with a pattern. The first group of four angles is exactly the same as the second group of four angles!

We wrote the following down in our notes:

If you want to see those patterns visually, check out the video…

In class, you should have finished at least #1-7. There is no additional homework!

Wednesday, 5/31: Triangle Similarity (Day 3 of 14)

Learning Target: Work with triangles in order to explore their angle relationships.
Handouts: Triangle Similarity (Turn in: Thurs, 6/1)

Today we worked with similar polygons. Remember, similar polygons have the same shape but are different sizes – like when we drew dilations in our last unit! You already know that if you have two similar triangles, you can use the scale factor to find the unknown side lengths. Today though, we worked with similar triangles and our focus was on their interior angles.

My demonstration in class showed you that when you enlarge or shrink a triangle, even though the side lengths changes, the angles all stay the same! So if each of the angles in one triangle have the same measure as each of the angles in another triangle, then the two triangles are similar. We don’t even need to look at the lengths of the sides!

As you worked through the classwork, you found a shortcut with the angles on #2. You found that if a pair of triangles have two angle measures in common, then the third angles must be equal too! Therefore, when you have a pair of triangles with two sets of equal angles, then the two triangles are similar!

Your homework is to make sure you have #1-7 complete.

Tuesday, 5/30: Triangles and Angles (Day 2 of 14)

Learning Target: Work with triangles in order to explore their angle relationships.
Handouts: Triangles and Their Angles (Turn in: Wed, 5/31)

Today we looked at angles in triangles. We started by taking down some notes:

We know that the interior angles of a triangle always add up to 180 degrees. So if we know the measures of two of the angles, we can always find the measure of the third!

Finding the measures of exterior angles requires just a little more thought. The exterior angle and the angle next to it will always form a straight line, so the two angle measures must add up to 180 degrees. Then if we know the measure of one of the two angles, we can find the measure of the other.

Your homework is to finish #1-6.

Friday, 5/26: Angle Measures in Geometry (Day 1 of 14)

Learning Target: Use angle relationships to find angle measures.
Handouts: Angle Measures (Turn in: Tues, 5/30)

Today we started our geometry unit! You got a new packet of notes, and we filled in the front page with some definitions and examples:

Geometry is a subject that is very vocabulary heavy and also contains a lot of symbols, so pay attention to these things! It is also very logical, so work through the problems step-by-step and use the angle relationships that we discussed in our notes!

In class, you should have completed at least #1-5. There is no additional homework, so have a great three-day weekend!