B Apply

Graph and label each triangle with the given vertices. Determine whether each triangle is scalene, isosceles, or equilateral. Then tell whether each triangle is a right triangle.

17. T(1, 1), R(3, 8), I(6, 4)
18. J( − 5 , negative 5 comma 0), K(5, 8), L ( 4 , − 1 ) l open 4 comma negative 1 close
19. A(3, 2), B ( − 10 , b open negative 10 comma 4), C ( − 5 , − 8 ) c open negative 5 comma negative 8 close
20. H(1, − 2 negative 2 ), B( − 1 , negative 1 comma 4), F(5, 6)

Graph and label each quadrilateral with the given vertices. Then determine the most precise name for each quadrilateral.

21. P( − 5 , negative 5 comma 0), Q( − 3 , negative 3 comma 2), R(3, 2), S(5, 0)
22. S(0, 0), T(4, 0), U(3, 2), V( − 1 , negative 1 comma 2)
23. F(0, 0), G(5, 5), H(8, 4), I(7, 1)
24. M( − 14 , negative 14 comma 4), N(1, 6), P(3, − 9 negative 9 ), Q ( − 12 , − 11 ) q open negative 12 comma negative 11 close
25. A(3, 5), B(7, 6), C(6, 2), D(2, 1)
26. N( − 6 , negative 6 comma 4), P( − 3 , negative 3 comma 1), Q(0, 2), R( − 3 , negative 3 comma 5)
27. J(2, 1), K(5, 4), L(8, 1), M(2, − 3 negative 3 )
28. H ( − 2 , − 3 ) , h open negative 2 comma negative 3 close comma I(4, 0), J(3, 2), K ( − 3 , − 1 ) k open negative 3 comma negative 1 close
29. W( − 1 , negative 1 comma 1), X(0, 2), Y(1, 1), Z(0, − 2 negative 2 )
30. D( − 3 , negative 3 comma 1), E ( − 7 , − 3 ) , e open negative 7 comma negative 3 close comma F(6, − 3 negative 3 ), G(2, 1)

31. Think About a Plan Are the triangles below congruent? How do you know?

    

    • Which triangle congruence theorem can you use?
    • Which formula should you use?
32. Reasoning A quadrilateral has opposite sides with equal slopes and consecutive sides with slopes that are negative reciprocals. What is the most precise classification of the quadrilateral? Explain.

Determine the most precise name for each quadrilateral. Then find its area.

33. A(0, 2), B(4, 2), C ( − 3 , − 4 ) , D ( − 7 , − 4 ) c open minus , 3 comma negative 4 close comma , d open minus , 7 comma negative 4 close
34. J(1, − 3 negative 3 ), K(3, 1), L(7, − 1 negative 1 ), M(5, − 5 negative 5 )
35. D E ¯ d e bar is a midsegment of Δ A B C cap delta eh b c below. Show that the Triangle Midsegment Theorem holds true for Δ A B C . cap delta eh b c .

    

36. 1. Writing Describe two ways you can show whether a quadrilateral in the coordinate plane is a square.
    2. Reasoning Which method is more efficient? Explain.

37. Interior Design Interior designers often use grids to plan the placement of furniture in a room. The design shows four chairs around a coffee table. The designer plans for cutouts of chairs on lattice points. She wants the chairs oriented at the vertices of a parallelogram. Does she need to fix her plan? If so, describe the change(s) she should make.

    

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