1) Given: \(\triangle ABC\) and \(\triangle DEF\) with coordinates \(A(1, 8), B(-3, 1), C(1, 1), D(-3, -2), E(-3, -6)\) and \(F(4, -6)\)
Prove: \(\triangle ABC\cong\triangle FDE\)
2) Given: \(\triangle ABC\) with coordinates \(A(0, 4), B(-3, 0), C(3, 0)\) and \(D(0, 0)\)
Prove: \(\overline{AD}\) bisects \(\angle BAC\)
3) Prove that the midpoint of the hypotenuse in a right triangle is equidistant from the three vertices of the triangle.
4) Given: \(D, E,\) and \(F\) are midpoints of the sides of equilateral \(\triangle ABC\)
Prove: \(\triangle DEF\) is equilateral
5) \(\triangle ABC\) is a right isosceles triangle with hypotenuse \(\overline{AB}\). \(D\) is the midpoint of \(\overline{AB}\).
a. Prove that \(\overline{CD}\perp\overline{AB}\)
b. Describe two methods you could use to prove \(\triangle CAD\cong\triangle CBD\)
Prove: \(\triangle ABC\cong\triangle FDE\)
2) Given: \(\triangle ABC\) with coordinates \(A(0, 4), B(-3, 0), C(3, 0)\) and \(D(0, 0)\)
Prove: \(\overline{AD}\) bisects \(\angle BAC\)
3) Prove that the midpoint of the hypotenuse in a right triangle is equidistant from the three vertices of the triangle.
4) Given: \(D, E,\) and \(F\) are midpoints of the sides of equilateral \(\triangle ABC\)
Prove: \(\triangle DEF\) is equilateral
5) \(\triangle ABC\) is a right isosceles triangle with hypotenuse \(\overline{AB}\). \(D\) is the midpoint of \(\overline{AB}\).
a. Prove that \(\overline{CD}\perp\overline{AB}\)
b. Describe two methods you could use to prove \(\triangle CAD\cong\triangle CBD\)