1.	Which statement can be used to show that if is a median of ?
		A.	The median of an isosceles triangle is a perpendicular bisector of the base. So, by definition of bisector, .
		B.	and . Therefore, because corresponding parts of congruent angles are congruent.
		C.	The median of an isosceles triangle bisects the vertex angle. So, the segments opposite the angles are congruent.
		D.	because and are reflections of each other.
		Hint
	2.	Complete the paragraph proof. If , and , then .
		A.	by SAS. So, because they are corresponding parts of congruent triangles. by the reflexive property. So, because the sides of both angles are congruent.
		B.	by SAS. So, because they are corresponding parts of congruent triangles. Because and , you know that is a median of , and that is a median of . Thus, by SAS. So, because they are corresponding parts of congruent triangles.
		C.	by SAS. So, because they are corresponding parts of congruent triangles. is an isosceles triangle because it has two congruent sides. So, because the base angles of an isosceles triangle are congruent.
		D.	by SAS. So, because they are corresponding parts of congruent triangles. By angle addition, or . In , or . So by substitution, . So, by the property of equality.
		Hint
	3.	If and , show that .
		A.	You know that and . and are congruent because they are vertical angles. Thus, by ASA.
		B.	You know that and . Point C is the midpoint of since . That means that C is also the midpoint of . So by definition of midpoint. Therefore, by SSA.
		C.	You know that and . because and are congruent alternate interior angles. So, by SAS.
		D.	You know that and . because they are alternate interior angles, and because they are vertical angles. So, by AAA.
		Hint
	4.	Write a paragraph proof to prove .
		A.	Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel. and because they are alternate interior angles. Also, because they are opposite angles of a parallelogram. Thus, by AAA.
		B.	There is not enough information provided, so it is not possible to prove .
		C.	Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel. Opposite sides of a parallelogram are congruent, so and . Also, opposite angles of parallelograms are congruent so . Therefore, by SAS.
		D.	Quadrilateral PQRS is a parallelogram because both pairs of opposite sides are parallel. Since quadrilateral is a parallelogram, by definition.
		Hint
	5.	Write a paragraph proof for the conjecture. If quadrilateral ABCD is an isoceles trapezoid, and and are diagonals, then .
		A.	You know that quadrilateral ABCD is an isosceles trapezoid. That means that because the legs of an isosceles trapezoid are congruent. Also, because the base angles of an isosceles trapezoid are congruent. By the reflexive property, . So, by SAS.
		B.	You know that quadrilateral ABCD is an isosceles trapezoid. That means that because the legs of an isosceles trapezoid are congruent. Also, because the base angles of an isosceles trapezoid are congruent. By the reflexive property, . So, by SAS.
		C.	You know that quadrilateral ABCD is an isosceles trapezoid. by definition of a trapezoid. Also, because the legs of an isosceles trapezoid are congruent. and because they are alternate interior angles. So, by ASA.
		D.	You know that quadrilateral ABCD is an isosceles trapezoid. That means that because the diagonals of an isosceles trapezoid are congruent. So, by SSS.
		Hint