Geometry Notes Review: Section's 8.1 and 8.2

​Section 8.3 - Review: The Pythagorean Theorem & The Converse of the pythagorean theorem.

​Lesson Target

Students will be able to
1. Identify and describe the differences and similarities between the pythagorean theorem and the converse of the pythagorean theorem
2. Describe how the pythagorean theorem is a calculation and the converse of the pythagorean theorem is a proof.
3. Find the legs of a triangle given two or three sides of a triangle.

​Section 8.3 - Review: The Pythagorean Theorem & The Converse of the pythagorean theorem.

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

First, What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

The Pythagorean Theorem: A "calculation" in finding the missing side lengths

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

The Pythagorean Theorem: A "calculation" in finding the missing side lengths

Multiple Choice

Use the image to answer the question

• c = 5

• c = 10

• c = 20

• c = 1

Multiple Choice

Use the image to answer the question

• c = 10

• c = 13

• c = 18

• c = 24

Multiple Choice

Use the image to answer the question

• a = 2

• a = 5

• a = 7

• a = 8

Multiple Choice

Use the image to answer the question

• a = 12

• a = 15

• a = 17

• a = 18

Multiple Choice

Use the image to answer the question

• b = 6

• b = 8

• b = 12

• b = 13

Multiple Choice

Use the image to answer the question

• b = 26

• b = 28

• b = 24

• b = 13

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

The Pythagorean Theorem: A "calculation" in finding the missing side lengths

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

The Converse of the pythagorean theorem: verifies whether a triangle is a right triangle and what type of triangle the figure is...

​Section 8.2 Part 2: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: What is the converse of the pythagorean theorem?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Using the converse of the pythagorean theorem when given three sides to determine if it is a right triangle...

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Using the converse of the pythagorean theorem when given three sides to determine if it is a right triangle...

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Using the converse of the pythagorean theorem when given three sides to determine if it is a right triangle...

Multiple Choice

Use the image to answer the question

• Yes, the following sides create a right triangle

• No, the following sides do not create a right triangle

Multiple Choice

Determine if a triangle with sides 4, 7, and 8 is a right triangle?

• Yes, the following sides create a right triangle

• No, the following sides do not create a right triangle

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side lengths to determine if a triangle is a right triangle?

Multiple Choice

If the given triangle has two side lengths of a = 5 and b = 12, find the third side that would make the triangle a right triangle.

• c = 17

• c = 7

• c = 13

• c = 3

Multiple Choice

If the given triangle has two side lengths of a = 9 and b = 10, find the third side that would make the triangle a right triangle.

• c = 13.45

• c = 7.81

• c = 13.85

• c = 3.21

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, To find the missing side length of a triangle that will create a right triangle with given shorter sides

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, To find the missing side length of a triangle that will create a right triangle with given shorter sides

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, To find the missing side length of a triangle that will create a right triangle with given shorter sides

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, To find the missing side length of a triangle that will create a right triangle with given shorter sides

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, To find the missing side length of a triangle that will create a right triangle with given shorter sides

Multiple Choice

If a triangle has side lengths a = 6 and b = 10, what side length for "c" would create a right triangle?

• c = 10.22

• c = 11.66

• c = 12.81

• c = 13.21

Multiple Choice

If a triangle has side lengths a = $$2\ \frac{3}{4}$$ and b = $$5\ \frac{1}{2}$$ , what side length for "c" would create a right triangle?

• c = 6.15

• c = 7.21

• c = 8.22

• c = 9.12

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, Find the missing side length of the right triangle when given the longer sides of the triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, Find the missing side length of the right triangle when given the longer sides of the triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, Find the missing side length of the right triangle when given the longer sides of the triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, Find the missing side length of the right triangle when given the longer sides of the triangle?

Multiple Choice

If a given triangle has two longer sides of 8 and 10, what would be the missing side length of the triangle to create a right triangle?

• a = 2

• a = 4

• a = 6

• a = 8

Multiple Choice

If a given triangle has two longer sides of 12 and 13, what would be the missing side length of the triangle to create a right triangle?

• a = 2

• a = 4

• a = 5

• a = 8

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side lengths to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given three side length to determine if a triangle is acute, obtuse, or right? (Converse of the P.T.)

Multiple Choice

Determine if the following triangle is acute, obtuse, or right given the following three sides:

6, 7, and 8?

• 85 > 64, thus the triangle is acute

• 85 < 144, thus the triangle is obtuse

• 85 = 85 thus the triangle is a right triangle

Multiple Choice

Determine if the following triangle is acute, obtuse, or right given the following three sides:

6, 8, and 11?

• 100 > 98 thus the triangle is acute

• 100 < 121, thus the triangle is obtuse

• 100 = 100 thus the triangle is a right triangle

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Now, what happens if you are given two side length to determine if a triangle creates a right triangle, obtuse triangle, or acute triangle?

Multiple Choice

Let's say you are given a plot of land with two known sides of your land which are 2 and 5 acres. You would like to "add" more land, but you are unsure what shape of triangle you would like your lang to form. Identify if the land you will own creates an acute, right, or obtuse triangle within the given information above.

• acute: 3 < c < 5.39 acres

  obtuse: 5.39 < c < 7

  right: c = 5.39

• acute: 5.39 < c < 3 acres

  obtuse: 5.39 < c < 7

  right: c = 3

• acute: 3 < c < 5.39 acres

  obtuse: 5.39 < c < 7

  right: c = 7

• acute: 5.39 < c < 5.39 acres

  obtuse: 3 < c < 7

  right: c = 5.39

Multiple Choice

You are a surveyor for a company who can estimate how much land is within a given area and size. You are surveying a lang for a company who wants their main set of land as an obtuse triangle. The two sides of the surveyed land are 12 and 16 acres. What is the third side length range to create an obtuse triangle for the company?

• 10 < c < 18

• 20 < c < 28

• 21 < c < 30

• 24 < c < 32

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "longer" sides of a triangle?

Multiple Choice

Classify the following triangle as acute, obtuse, or right if given the two larger sides:

8, 10

• Triangle Inequality: 2 < a < 18

  Acute: 6 < a < 18

  Right: a = 6

  Obtuse: 2 < a < 6

• Triangle Inequality: 2 < a < 18

  Acute: 2 < a < 6

  Right: a = 18

  Obtuse: 6 < a < 18

• Triangle Inequality: 2 < a < 18

  Acute: 2 < a < 6

  Right: a = 6

  Obtuse: 6 < a < 18

• Triangle Inequality: 2 < a < 18

  Acute: 6 < a < 18

  Right: a =18

  Obtuse: 2 < a < 6

Open Ended

Classify the following triangle as acute, obtuse, or right if given the two larger sides:

7, 13

Multiple Choice

Monopoly - You just inherited a triangular piece of land yay! The two larger sides of your land are 8 and 18. Using the given data, identify the type of triangle you could create (acute, obtuse, right) if you were to extend your plot of land (or decrease).

• For the given piece of land:

  1. Acute: 16.2 < a < 26

  2. Obtuse: 10 < a < 16.2

  3. Right: 16.2

• For the given piece of land:

  1. Acute: 12.4 < a < 24

  2. Obtuse: 10 < a < 12.4

  3. Right: 12.4

• For the given piece of land:

  1. Acute: 16.2 < a < 21

  2. Obtuse: 10 < a < 16.2

  3. Right: 21

• For the given piece of land:

  1. Acute: 16.2 < a < 18

  2. Obtuse: 10 < a < 14.2

  3. Right: 18

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

​S​Section 8.3: Identifying Acute, Obtuse & Right Triangles using the P.T. and the Converse of the P.T.

Review: How do I find out if a triangle is acute, obtuse, or right given 2 sides that are the "shorter" sides of a triangle?

Multiple Choice

Classify the following triangle as acute, obtuse, or right if given the two smaller sides:

8, 10

• Acute: 2 < c < 12.8

  Right: 2

  Obtuse: 12.8 < c < 18

• Acute: 8 < c < 12.8

  Right: 12.8

  Obtuse: 12.8 < c < 18.2

• Acute: 4 < c < 12.8

  Right: 12.8

  Obtuse: 12.8 < c < 16

• Acute: 2 < c < 12.8

  Right: 12.8

  Obtuse: 12.8 < c < 18

Open Ended

Classify the following triangle as acute, obtuse, or right if given the two smaller sides: 7, 13. Attach your work

Poll

I am ready for the homework pertaining to section's 8.1 and 8.2?

• Yes

• No

• Maybe

• I am so lost!