Polygons A-F, Summaries of Design

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Polygons A-F

An Introduction to Symmetry

Classifying Angles

Review

In a previous lesson, unit angles known as “wedges” were

used to measure angles. Another unit angle known as the

“degree” can also be used.

STRAIGHT ANGLE

ACUTE

ANGLES

OBTUSE

ANGLES

RIGHT

ANGLES

Classifying Angles

Using Degrees

If there are 360 degrees (360º) in a complete circle,

and 180 degrees (180º) in a straight angle,

how many degrees are in a right angle? _______

The right angle (90º) is a reference point for acute and

obtuse angles. Use what you know about acute and obtuse

angles to complete the chart below.

Angle Example Degrees

(Circle one)

Acute

Less than 90º

Greater than 90º

Acute

Less than 90º

Greater than 90º

Obtuse

Less than 90º

Greater than 90º

Obtuse

Less than 90º

Greater than 90º

RIGHT

ANGLES

ACUTE

ANGLES

OBTUSE

ANGLES

The “Fun” Polygon

Use these seven triangles and the “Classification and

Measurement Chart” as you complete the following steps.

Step 1: Classify each angle as “acute,” “right,” or “obtuse.” Step 2: Measure and record the length of each side.

a

b c

2. a

b c

a

b c

a b

c

a

b

c

6. a

b c

a b

c

Answer Key

Classification and Measurement Chart

Triangles Angle Classifications Side Measurements* Draw a similar version of each triangle below. (^) a b c ab bc ca

Acute Acute Acute 3.4 cm 3.4 cm 3.4 cm

ACUTE EQUILATERAL

Acute Right Acute 5.3 cm 2.5 cm 5.9 cm

RIGHT SCALENE

Acute Acute Acute 2.9 cm 2.3 cm 2.7 cm

ACUTE SCALENE

Right Acute Acute 3.9 cm 5.5 cm 3.9 cm

RIGHT ISOSCELES

Acute Obtuse Acute 3.8 cm 3.8 cm 6.3 cm

OBTUSE ISOSCELES

Acute Acute Acute 6.2 cm 3.8 cm 6.2 cm

ACUTE ISOSCELES

Acute Acute Obtuse

cm 3.4 cm^ 9.3 cm

OBTUSE SCALENE

Trying Triangles

Directions:

Try your hand at building triangles! Using toothpicks, pipe

cleaners, pencils, or other line segments of your choice,

identify which of the following triangles can be constructed.

Is it possible to construct a triangle with…

Criteria YES NO Evidence

Similar drawings

One acute angle?

Two acute angles?

Three acute angles?

One right angle?

Two right angles?

Three right angles?

One obtuse angle?

Two obtuse angles?

Three obtuse angles?

The “Fun” Polygon

Manipulatives

Copy polygons onto cardstock paper for sturdier manipulative pieces.

Tricky Triangles

Directions:

Find the measures of the missing angles without using a protractor.

Use the following problem-solving steps to guide your work:

• Understand the Problem
• Decide on a Plan
• Carry out the Plan
• Look Back and Review

Step 1: Restate the problem in your own words:_________________________

---

________________________________________________________________________

List any questions you have at this time:________________________________

---

---

Jot down any hypotheses you have at this point:_________________________

---

---

Share your questions and hypotheses with others.

22º

73º 60º

60º

140º

27º

27º ? 45º

? ?

True Triangles

Use the following problem-solving steps to guide your work:

• Understand the Problem
• Decide on a Plan
• Carry out the Plan
• Look Back and Review

Step 1: Restate the problem in your own words:

List any questions you have at this time:

Jot down any hypotheses you have at this point:

Share your questions and hypotheses with others.

Step 2: List the first steps you plan to take in order to solve the problem:

“The sum of the lengths of any two sides of a triangle has

to be greater than the third side.” True or False?

Step 3: Carry out the Plan Possible manipulatives: Use straws cut into lengths of 2 cm, 3 cm, 5 cm, and 6 cm, or the strips provided below.

Step 4: Look Back and Review Collect and record the data gathered during each step. If new questions arise, adjust your plan to solve them. Remember to “look back” after each step. Ask yourself, “So, what does this tell me? What can I learn? What do I need to do next?”

Problem:

“The sum of the lengths of any two sides of a triangle has to be

greater than the third side.” True or False?

My Solution: Explain your answer in paragraph form.

Label the strips (2, 3, 5, or 6 cm) and then cut them out to test your hypotheses.

Transformation #2: Flips

A polygon can be flipped horizontally or vertically. This

movement is called a “flip” or a “reflection.”

Example: Horizontal Flip

The pattern is reflected (or mirrored) beside the original shape.

How would your triangle look if it was flipped horizontally?

Example: Vertical Flip

The pattern is reflected (mirrored) below or above the original shape.

How would your triangle look if it were flipped vertically?

above

START HERE

below

START HERE

Equilateral Triangles

Manipulatives

Part B

3. Draw one, two, and three lines of symmetry on the triangles below. (Fold and manipulate the paper triangle as needed.)

Lines of Symmetry

One Line Two Lines Three Lines

a. b. c.

4. Identify the congruent triangles that are formed within each of the three triangles and label them with a C.

Part C (Extra Credit)

5. Select one of the triangles above, and redraw its line(s) of symmetry in the similar version below.
6. Create a simple design on one of the congruent triangles.
7. Show the flipped version (or a reflection) of that triangle on the other congruent triangle.
8. Use a dashed line ( ) and a curved arrow ( ) to show how the figure was flipped.

Scoring Criteria

Part A

1. 20 points Students complete the chart using the following vocabulary words (5 points per pair): Triangle1: acute – isosceles Triangle 3: obtuse - isosceles Triangle 2: acute – equilateral Triangle 4: right - scalene

2a. The content of the paragraph is assessed as follows: 20 points Students include specific details and vocabulary to explain how triangles are named. See the adapted Long-Answer Question rubric below to understand what a “clear and complete” answer looks like for this prompt (# of points x 5).

4 points 3 points 2 points 1 point

Explaining

Your

Answer

Your explanation is so clear and complete that the reader can use the specific details and vocabulary you provide to correctly name new triangles.

Your explanation is clear and complete. It is supported by specific and appropriate vocabulary. It is clear to the reader why the triangles have these names.

Your explanation is hard to follow. Appropriate vocabulary may be used, but specific details are lacking. It is hard for the reader to understand how triangles are named.

Your explanation is unclear and/or incomplete. It contains inappropriate or insufficient vocabulary. The reader is confused about how triangles are named.

2b. The format of the paragraph may be assessed as follows: 5 points Students begin the paragraph with an introductory sentence. 15-20 points Students develop supporting ideas by presenting facts and information that clearly relate to the focus (5 points per supporting fact or piece of information). 5 points Students conclude the paragraph.

Part B

3. 15 points Students identify and draw three lines of symmetry (5 points per line).
4. 15 points Students identify and label congruent figures in each triangle (5 points per triangle).

Part C (Extra Credit)

5. 1 point Students redraw the line(s) of symmetry.
6. 1 point Students create a simple design on one congruent figure.
7. 6 points Students accurately reflect (flip) the congruent figure.
8. 2 points Students show the line over which the figure was flipped.