12/03/2024 - HG-Triangles Coordinate Plane/Classify

Draw

The following plexers are of common sayings. Study the pictures to determine at least three plexers.

Poll

Would you rather have the ability to see 10 minutes into the future or 150 years into the future?

I will use our Wheel of Names to choose someone to "Shore Out"

• see 10 minutes into the future

• 50 years into the future

Essential Questions

● How can you use coordinate geometry to classify triangles and solve real-world problems?

Triangles & Coordinate Geometry

Multiple Choice

What is the distance between American Eagle and the Barnes and Nobles?

• 12 feet

• 14 feet

• 10cfeet

• 16 feet

Multiple Choice

What is the distance between JC Penny and the Movie Theater?

• 15 feet

• 14 feet

• 2 feet

• 8 feet

​Now, back to Triangles!

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

​Triangle Inequalities

Multiple Choice

Determine if the three numbers can be measures of the sides of a triangle. 9, 11, 2

• Yes

• No

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

Multiple Choice

Can the side lengths 4, 9 and 16 form a triangle?

• Yes

• No

Multiple Choice

State if the three side lengths form an acute, obtuse, or right triangle.

• Acute

• Obtuse

• Right

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

Multiple Choice

State if the three side lengths form an acute, obtuse, or right triangle.

• Acute

• Obtuse

• Right

Finding Perimeter of a Triangle

Side 1 + Side 2 + Side 3 = P
a + b + c = P
OR
P = Side 1 + Side 2 + Side 3
P = a + b + c

Draw

Highlight the parts of the triangle you would need to find the PERIMETER of the triangle. (You do not need to find the perimeter.)

Draw

Use the image to find the perimeter of the triangle.

Step 1: Choose a side.

Step 2: Use the distance formula to find the length of the side.

Step 3: Write the length of the side on the image.

Step 4: Repeat steps 1 through 3 for the other two sides.

Be sure to show the FIRST step of the distance formula for the hypotenuse.

(show where the numbers are substituted in the formula)

Write the perimeter in the top LEFT corner.

​

​√(8-8)² + (9-1)²
√ (0)² + (8)²
√0 + 64
√64
8
(you also could have just counted)

​√(8-2)² + (1-1)² = √(6)² + (0)² = √36 + 0 = √36 = 6
(you also could have just counted)

​√(8-2)² + (9-1)²
√(6)² + (8)²
√36 + 64
√100
10

​Check your work!

​P = 6+8+10 = 24 units

Draw

Find the perimeter of the triangle.

Step 1: Choose a side.

Step 2: Use the distance formula to find the length of the side.

Step 3: Write the length of the side on the image.

Step 4: Repeat steps 1 through 3 for the other two sides.

Be sure to show the FIRST step of the distance formula for the hypotenuse.

(show where the numbers are substituted in the formula)

Write the perimeter in the top LEFT corner.

If necessary, round to the nearest thousandths.

​

​(1,1)

​(1,7)

​(6,1)

​P = 5+6+7.810 = 18.81 units

​Perimeter with Expressions

Let's Find the Perimeter of this Triangle

• First, write your work out:

• Side 1 + Side 2 + Side 3

• x + x + 4 + x + 6

• What method can I use to simplify this expression?

Hopefully you said Combine Like Terms

• x + x + 4 + x + 6

• Combine your "x" terms

• Then Combine your constants

• 3x + 10

• Are we Done?

Multiple Choice

Is the perimeter of this triangle 3x + 10

• yes

• no

Multiple Choice

Which expression represents the perimeter of the triangle?

• 4x + 4y + 5
• 6xy + 7
• 6x + 2y + 5
• 10xy + x + 2y

Multiple Choice

The perimeter of the triangle is 10x + 20. Find the length of the missing side.

• 6x+10
• 15x+30
• 5x+10
• 5x-10

​a

b

h

c

A = 1/2 (5)(12)
A = 1/2 (60)​
(you may multiply in the order you prefer)
A = 30 square units
30 units²

height

Draw

Highlight the parts of the triangle you would need to find the AREA of the triangle. (You do not need to find the area.)

Multiple Choice

What is the area of the triangle?

• 33 sq. units

• 66 sq. units

• 37 sq. units

• 74 sq. units

Draw

What is the area of the triangle?

Be sure to write the length of the base and height on the image.

Show your work on how to find the area of the triangle. Write neatly.

Multiple Choice

A triangle has a base of 9 feet and a height of 13 feet. What is the area of the triangle?

• 58 sq. ft.

• 117 sq. ft.

• 58.5 sq. ft.

• 585 sq. ft

Multiple Choice

Find the area of the triangle.

• A = 40m

• A = 20m

• A= 11m +8 

• A = 14m

​Independent Practice

Multiple Select

Classify the triangle by sides and angles (choose two answers).

• Right triangle

• Acute triangle

• Obtuse triangle

• Equilateral triangle

• Isosceles triangle

Multiple Select

Classify the triangle by both sides and angles (choose two answers).

• Right triangle

• Acute triangle

• Obtuse triangle

• Isosceles triangle

• Scalene triangle

Fill in the Blank

Given the coordinates, classify ΔJKL by its sides.

$$J\left(-3,\ 2\right),\ K\left(2,\ 6\right),\ L\left(8,\ -1\right)$$  

Fill in the Blank

Given the coordinates, classify ΔDEF by its sides.

$$D\left(-2,\ 3\right),\ E\left(5,\ 5\right),\ F\left(-4,\ 10\right)$$  

Multiple Choice

Find x.

• 52

• 104

• 26

Fill in the Blank

Given its coordinates, classify ΔFGH

$$F\left(-5,\ 10\right),\ G\left(-2,\ 2\right),\ H\left(-9,\ -7\right)$$  

Multiple Choice

If LN = 5, then AC = ______.

• 5
• 10
• 15
• 25

Multiple Choice

Is DE parallel to BC?

• Yes
• No

Multiple Choice

Find the perimeter of this triangle.

• 150 ft
• 100 ft
• 20 ft
• 35 ft

Multiple Choice

Given that A(-2,3), B(4,1) and C(2,-4) are vertices of a triangle, find the perimeter of the triangle.

• 20.789

• 19.772

• 23.9

• 13.456

Multiple Choice

Find the perimeter of this triangle.

• 12 in
• 22 in
• 18 in
• 24 in

Multiple Choice

Ordered pair (0,0) is also known as the ___.

• y-axis
• x-axis
• origin

Multiple Choice

Points G, H, and I are plotted on the coordinate grid. What is the perimeter (in units) of the triangle that they form?

• 16.64

• 39.64

• 126

• 63

Multiple Choice

Given that P(-4, -2), Q(-2, 2) and R(5, 1) are vertices of a triangle, calculate the perimeter and classify the triangle.

• 21.1, Isosceles

• 21.1, Scalene

• 24.3, Scalene

• 24.3, Equilateral

Multiple Choice

Calculate the length for each side of the triangle.

• AB = 3.6, BC = 4.5, AC = 4.1

• AB = 4.1, BC = 5.6, AC = 7.5

• AB = 4.5, BC = 3.6, AC = 4.1

• AB = 4.1, BC = 3.6, AC = 4.5

Multiple Choice

Is EFG a right triangle given E(0,1), F(2,3) and G(4,-1)?

• Yes, because two sides are perpendicular.

• No, there are no perpendicular sides

• Yes, because two sides are parallel.

• No, because no two sides are equal length.

Multiple Choice

If a triangle with vertices of (-3,0), (0,3), (3,0), classify it by its sides/

• Isosceles

• Scalene

• Equilateral

• Obtuse

Multiple Choice

Find the measure of <A.

• 180
• 70
• 54
• 56

Multiple Choice

Find the measure of the indicated angle. 

• 34
• 46
• 62
• 36

Multiple Choice

How is the distance formula correctly written:

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$$

• $$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}$$

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$$

• d = $$\sqrt{\left(x\right)^2-\ \left(y\right)^2}$$

Multiple Choice

Find x.

• 54

• 200

• 50

• 46

Multiple Choice

What is the opposite of squaring a number?

• divide
• multiply 
• fractions
• square root

Multiple Choice

Find the direct distance between the court house and the town hall.

• 26
• 6.8
• 10
• 7.2 km

Multiple Choice

Write an equation of a line that passes through the point (-9,2) and is perpendicular to the line y = 3x - 12

• y = (-1/3)x - 1
• y = (1/3)x - 2
• y = -3x + 12
• y = 3x - 1

Multiple Choice

Use the picture to help you answer the question.
Make sure to:
-ID the legs and hypothenuse
-Plug in those values into $$a^2+b^2=c^2$$

-Simplify the exponents
-Get the variable by itself
-No need to take the square root this time:)

• $$\sqrt{29}$$

• $$\sqrt{40}$$

• $$\sqrt{65}$$

• $$\sqrt{72}$$

Multiple Choice

Use the picture to help you answer the question.
Make sure to:
-ID the legs and hypothenuse
-Plug in those values into $$a^2+b^2=c^2$$

-Simplify the exponents
-Get the variable by itself
-You may have to take the square root to find your answer

• 5 units

• 13 units

• $$\sqrt{65}$$

• $$\sqrt{97}$$

Multiple Choice

Click on the picture to see the question. Don't forget:

-ID your legs & hypothenuse
-Count the units of each leg 
-Plug in that information into   $$a^2+b^2=c^2$$  
-Simplify your exponents
-Get the variable on one side
-Take the square root 

• 8 units

• 12 units

• 15 units

• 21 units

Multiple Choice

Use the coordinate grid to answer questions about Carla's visit to the movie theater. If Carla is late to the movie and wants to take the quickest path (from point A to point B), how far will she have to travel?
HINT: Find the distance of both legs by counting the units AND THEN figure out the hypotenuse using... $$a^2+\ b^2=c^2$$  

• 7 units

• 8 units

• 9 units

• 12 units

Multiple Choice

Use the map of Sarah's town to answer the question below.

What is the distance Sarah will travel from her house to Randi's?

• 5 units

• 6 units

• 8 units

• 10 units

Multiple Choice

Use the map of Sarah's town to answer the question below.
What is the distance Sarah will travel from the store to her house? (Use the Pythagorean Theorem to help you  $$\alpha^2+b^2=c^2$$  )

• 5 units

• 6 units

• 8 units

• 10 units