Using Coordinate algebra, definitions, and properties 5D-3 Coordinate Proof Using Coordinate algebra, definitions, and properties

Property of a Liquid Takes the shape of the container while maintaining a constant volume

Liquid?

http://imgur.com/gallery/U0iADj9

A Right Triangle is a triangle with one right angle. What’s the definition, theorem or property? Prove that ∆𝐴𝐵𝐶 is a right triangle. A Right Triangle is a triangle with one right angle. Are there any right angles? Or perpendicular sides? What can you use to show this? Strategy: Find slopes of each side. Are they negative reciprocals? If yes, the two sides form a right angle. If there is one right angle, then it is a right triangle.

Proof: This is the format for a coordinate proof. Prove is a right triangle. Work Area: } 𝐴𝐵 𝑚= 𝑢𝑝 3 𝑜𝑣𝑒𝑟 4 = 3 4 𝐴𝐵 ⊥ 𝐵𝐶 𝐵𝐶 𝑚= 𝑑𝑜𝑤𝑛 4 𝑜𝑣𝑒𝑟 3 = −4 3 ∠𝐵 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒 Statement: Is a right triangle b/c is a right angle.

Prove ∆𝐴𝐵𝐶 is a right triangle. Work Area: } 𝐶𝐵 𝑚= 𝑢𝑝 3 𝑜𝑣𝑒𝑟 4 = 3 4 𝐶𝐵 ⊥ 𝐶𝐴 𝐶𝐴 𝑚= 𝑑𝑜𝑤𝑛 4 𝑜𝑣𝑒𝑟 3 = −4 3 ∠𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒 Statement: Is a right triangle, b/c ∆𝐴𝐵𝐶 ∠𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒

Prove ∆𝐴𝐵𝐶 is an isosceles triangle. Work Area: } 𝐶𝐵 𝑑= (5−1) 2 + (6−3) 2 = 5 𝐶𝐵 ≅ 𝐶𝐴 𝐶𝐴 𝑑= (4−1) 2 + (−1−3) 2 = 5 Statement: Is an isosceles triangle, b/c 𝐶𝐵 ≅ 𝐶𝐴 ∆𝐴𝐵𝐶

Prove ABCD is a parallelogram. Definition: Opposite sides are parallel. Slopes Property: Opposite sides are congruent. Distance formula You can choose either one, so which seems easier to prove?

Prove ABCD is a parallelogram. Work Area: Statement:

Prove ABCD is a rectangle. Definition: a Parallelogram with one right angle. Plan: first, prove it’s a parallelogram Second prove there is a right angle

Prove ABCD is a rectangle. Work Area: Statement: ABCD is a rectangle b/c ___________________ and ___________________

Definitions and Properties Right triangle: a triangle with one right angle Isosceles triangle: a triangle with two congruent sides Parallelogram: a) Quadrilateral with opposite sides parallel OR b) Parallelogram Property: Opposite sides congruent Rectangle: A parallelogram with one right angle

A Right Triangle is a triangle with one right angle. What’s the definition, theorem or property? A Right Triangle is a triangle with one right angle. Prove that ∆𝐴𝐵𝐶 is a right triangle. Are there any right angles? Or perpendicular sides? What can you use to show this? Strategy: Find slopes of each side. Are they negative reciprocals? If yes, the two sides form a right angle. If there is one right angle, then it is a right triangle.

Proof: This is the format for a coordinate proof. Prove is a right triangle. Work Area: _______ is a __________ __________ Statement: Is a right triangle b/c _________________________

Prove ∆𝐴𝐵𝐶 is a right triangle. Work Area: _______ is a __________ __________ Statement: Is a right triangle, b/c ∆𝐴𝐵𝐶 ∠𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒

Prove ∆𝐴𝐵𝐶 is an isosceles triangle. Work Area: Statement: is an isosceles triangle, b/c ___________ ∆𝐴𝐵𝐶

Prove ABCD is a parallelogram. Definition: Opposite sides are parallel. Slopes Property: Opposite sides are congruent. Distance formula You can choose either one, so which seems easier to prove?

Prove ABCD is a parallelogram. Work Area: Statement:

Prove ABCD is a rectangle. Work Area: Statement: ABCD is a rectangle b/c ___________________ and ___________________