4.7 triangles and coordinate proof

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Page 1: 4.7 triangles and coordinate proof

Triangles and Coordinate Proof

Page 2: 4.7 triangles and coordinate proof

Placing a rectangle in the coordinate plane

Place a 2-unit by 6-unit rectangle in the coordinate plane.

Solution Choose a placement that makes finding distances easy.

Two possible placements:

Page 3: 4.7 triangles and coordinate proof

Using the Distance Formula

• A right triangle has legs of 5 units and 12 units. Place the triangle in a coordinate plane. Label the coordinates of the vertices and find the length of the hypotenuse.

Page 4: 4.7 triangles and coordinate proof

Using the Midpoint Formula

Page 5: 4.7 triangles and coordinate proof

Writing Coordinate Proofs

Page 6: 4.7 triangles and coordinate proof

UTOV ||

OUOU ≅

Given, horizontal lines.

Definition of CongruenceOV = UT Transitive property of equality.

∠UOV ≅ ∠OUT Alternate Interior Angles Theorem

∆OTU ∆≅ UVO SAS Congruence Postulate

UTOV ≅

Reflexive property of congruence.

Writing Coordinate Proofs

Page 7: 4.7 triangles and coordinate proof

Homework

• Exercise 4.7 page 247: 1-27, 34.

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4.7 use isosceles and equilateral triangles

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4.7 – Isosceles Triangles

4.7 – Isosceles Triangles

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4.7 Isosceles and Equilateral Triangles

4.7 Isosceles and Equilateral Triangles

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Lesson 4-7 Triangles and Coordinate Proof

Lesson 4-7 Triangles and Coordinate Proof

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