1. Review

2. I can classify triangles using the coordinate plane (Sides)
Scalene
No sides are congruent.
Isosceles
Two or more sides are congruent.
Equilateral
All 3 sides are congruent.

3. To classify by sides use the distance formula or Pythagorean theorem to find the side lengths
What are the side lengths of the triangle?
What is the triangles classification based on sides?

4. Determine if the triangles is scalene, isosceles, or equilateral.

5. I can classify triangles using the coordinate plane (angles)
Right
0ne angle is exactly 90 degrees
Acute
All angles are smaller than 90 degrees
Obtuse
One angle is larger than 90 degrees

6. What are the slopes of the segments of the following triangle
What are the slopes of the segments of the following triangle? Is the triangle right, or not?

7. What about acute and obtuse triangles?
Determine a height line by drawing a perpendicular to the base through the other point. How do I know that the triangle is acute or obtuse?

8. Practice

9. Is a triangle right obtuse or acute? Construction
Explain how the circles and the lines came from the segment AB. Determine the regions where a point C would complete a right triangle ABC. Determine the regions where point C would complete an obtuse triangle ABC.

10. Is a triangle right obtuse or acute? Pythagorean theorem converse.
If 𝑎 2 + 𝑏 2 = 𝑐 2 then you have a right triangle
If 𝑎 2 + 𝑏 2 ≠ 𝑐 2 then you have an obtuse or an acute triangle.
Compare the right triangle to the obtuse triangle.
Has the 𝑎 2 + 𝑏 2 changed?
Has the 𝑐 2 changed?
Write an inequality to express when you have an obtuse triangle. 𝑎 2 + 𝑏 2 < 𝑐 2

11. Is a triangle right obtuse or acute? Pythagorean theorem converse.
If 𝑎 2 + 𝑏 2 = 𝑐 2 then you have a right triangle
If 𝑎 2 + 𝑏 2 ≠ 𝑐 2 then you have an obtuse or an acute triangle.
Compare the right triangle to the acute triangle.
Has the 𝑎 2 + 𝑏 2 changed?
Has the 𝑐 2 changed?
Write an inequality to express when you have an acute triangle. 𝑎 2 + 𝑏 2 > 𝑐 2

12. Determine if the following triangle is right obtuse or acute using the Pythagorean theorem.
1. find the distances of all the sides.
𝐴𝐵= 𝐵𝐶= 𝐴𝐶= 45
2. Put the distances into the Pythagorean theorem. Make sure the biggest number is the hypotenuse.
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So you have an obtuse triangle.

13. Practice If 𝑎 2 + 𝑏 2 = 𝑐 2 then right triangle If 𝑎 2 + 𝑏 2 < 𝑐 2 Then obtuse If 𝑎 2 + 𝑏 2 > 𝑐 2 Then acute

14. Find a 4th point that will complete the quadrilateral as it is given.
Rectangle
Parallelogram

15. Find a 4th point that would complete the trapezoid

16. Objective: given 4 ordered pairs determine what kind of quadrilateral it is.
Helpful formulas
Distance formula ________________________
Pythagorean theorem ______________________
Midpoint formula _________________________
Slope formula _________________________
Slopes of perpendicular lines relationship ______________________
Slopes of parallel lines relationship ___________________________

17. Trapezoid
Parallelogram
Rectangle
Square
Rhombus

18. 15.2 Determine what kind of quadrilateral
Parallelogram
If both pairs of opposite sides are congruent then it is a parallelogram.
If both pairs of opposite sides are parallel, then it is a parallelogram.
IF diagonals bisect each other then it is a parallelogram.

19. Prove that the quadrilateral with the coordinates L(-2,3) M(4,3), N(2,-2) and O (-4,-2) is a parallelogram.

20. Prove the quadrilateral with coordinates P(1,1), Q(2,4), R(5,6) and S(4,3) is a parallelogram.

21. Prove quadrilateral JOHN is a parallelogram
Prove quadrilateral JOHN is a parallelogram. J(-3,1),O((3,3), H(5,7) and N(-1,6)

22. Prove quadrilateral LEAP is a parallelogram
Prove quadrilateral LEAP is a parallelogram. L(-3,1),E(2,6), A(9,5) and P(4,0).

23. Rhombus
A rhombus is a special parallelogram.
If all sides are congruent it is a rhombus.
If the diagonals of a parallelogram are perpendicular then it is a rhombus.
If the adjacent sides of a parallelogram are a congruent, then it is a rhombus.

24. Prove that quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D (3,3) is a rhombus.

25. Prove that the quadrilateral with the vertices A(-1,4), B(2,6, C(5,4) and D(2,2) is a rhombus.

26. Rectangle
A rectangle is a special parallelogram.
If a parallelogram has diagonals that are congruent then it is a rectangle.
If a parallelogram has perpendicular line segments, then it is a rectangle.

27. Prove a quadrilateral with vertices g(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle.

28. Prove a quadrilateral with vertices C(0,0), O (5,2) A(5,2) and T(0,2) is a rectangle.

29. Square
A square is a rhombus and a rectangle. If you can show that the diagonals bisect each other,(parallelogram) are equal,(rectangle) and perpendicular(rhombus) then you know you have a square

30. Prove that the quadrilateral with vertices A(0,0) B(4,3), C(7,-1) and D(3,-4) is a square.

31. Prove that the quadrilateral with vertices A(2,2), B(5,-2), C(9,1) and D(6,5) is a square.

32. Trapezoid
If a shape is an isosceles trapezoid then one pair of sides is parallel. And the other pair is congruent.
If a shape is an isosceles trapezoid then one pair of sides is parallel and the diagonals are congruent.

33. Prove that quadrilateral MILK with the vertices M(1,3), I(-1,1), L (-1,-2) and K(4,3) is an isosceles trapezoid.

34. The vertices of quadrilateral MARY are M(-3,3), A(7,3), R(3,6) and Y(1,6). Prove that quadrilateral MARY is an isosceles trapezoid.

35. What kind of shape is it. Write the most specific shape.

36. Name that quadrilateral
A(4,4)B(6,2)C(8,4)D(6,6)
Test for parallelogram or trapezoid.
Test for rectangle, rhombus or isosceles trapezoid.
Test for square.

37. Name that quadrilateral
A(4,6)B(6,8)C(9,8)D(4,3)
Test for parallelogram or trapezoid.
Test for rectangle, rhombus or isosceles trapezoid.
Test for square.

38. Is Rice Eccles Field truly a rectangle?

40. Aerial view of the pentagon. Is the Pentagon a regular pentagon

41. Aerial view of Eiffel Tower. Does it form a perfect square?