Triangle Coordinate Proofs

Draw

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

Essential Questions

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

Classifying Right Triangles

• If c² = a² + b² --> right triangle

• If c² < a² + b² --> acute triangle

• If c² > a² + b² --> obtuse triangle

​Triangle Inequalities

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

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

height

External Angle Theorem

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​The exterior (supplement) to one angle is the sum of the other two interior angles

Reminder!!!

DE = 1/2(AB)

CE = BE

AD = DC

Multiple Choice

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

5ft, 8ft, 10ft

• Acute

• Obtuse

• Right

Draw

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

1) Graph and label each point.

2) Connect the points to make a triangle.

3) Write the length of each side of the triangle

4) Classify the triangle as acute, obtuse, or right.

5) Write the type of triangle in the top LEFT corner.

NOTE: EVERYONE's work will be displayed.

Draw

Given the coordinates, classify ΔJKL by its sides.

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

1) Graph and label each point.

2) Connect the points to make a triangle.

3) Write the length of each side of the triangle

4) Classify the triangle as acute, obtuse, or right.

5) Write the type of triangle in the top LEFT corner.

NOTE: Everyone's work will be displayed

Draw

The perimeter of the triangle is 10x + 20.

Find the length of the missing side.

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

What side(s) will always be the longest on a right triangle?

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Choice

What is the perimeter (in units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

• 65

• 8.06

• 14

• 19.06

Multiple Choice

What are the lengths of the triangle's sides?

• 6, 7, & 8

• 5, 5, & √7

• 5, 5, & √10

• 3, 4, & 5

Multiple Choice

What is the perimeter of the triangle? (Round to the nearest tenth)

• 12

• about 13.2

• 21

• about 12.6

Multiple Choice

What is the perimeter of the triangle? (Round to the nearest tenth)

• 12

• about 13.2

• 21

• about 12.6

Multiple Choice

What is the diagonal distance between the two points?

• 10.2 units
• 9.9 units
• 9.3 units
• 8.7 units

Multiple Choice

Find the distance between the two points.

• 2.2 units
• 3.5 units
• 4.1 units
• 2.7 units

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

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

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 perimeter of this triangle.

• 150 ft
• 100 ft
• 20 ft
• 35 ft

Multiple Choice

Find the area?

• 15 in²
• 30 in²
• 15 in
•  30 in

Multiple Choice

What segment is parallel to EF?

• Segment PM
• Segment MN
• Segment NP
• Segment FG

Multiple Choice

QR is a midsegment of triangle WUV. What is the length of segment QR?

• 4
• 8
• 16
• 32

Multiple Choice

Name a segment that has the same length as segment BD

• segment BE
• segment DE
• segment AD
• segment AC

Multiple Choice

If LN = 5, then AC = ______.

• 5
• 10
• 15
• 25

​Hump Day! Wednesday
December 4, 2024