Figure EFGH on the grid below represents a trapezoidal plate at its starting position on a rotating surface: A trapezoid EFGH drawn on a 4 quadrant coordinate grid with vertices E is at negative 4, 8. F is at negative 7, 5. G is at negative 4, 3. H is at negative 2, 5. The plate is rotated 90° about the origin in the counterclockwise direction. In the rotated trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?

3x + 4y = 5 x- 3y = -7 solve by substitution

2x minus y equals 6, x plus y equals negative 3

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)