11/13/ : Proving Quadrilateral Props 4.5: Proving Quadrilateral Properties Expectations: G1.4.2: Solve multi-step problems and construct proofs involving quadrilaterals. G2.3.1: Prove triangles are congruent. G2.3.2: Use congruent triangles to prove additional theorems. L3.3.1: Know the basic format of an proof.

11/13/ : Proving Quadrilateral Props In the figure below, AC is the diameter of the circle, B is a point on the circle, AB is congruent to BC and D is the midpoint of AC. What is the degree measure of angle ABD? A.30° B.45 C.60 D.90 E.Cannot be determined from the given information A D C B

11/13/ : Proving Quadrilateral Props Kites Defn: A quadrilateral is a kite iff it has 2 distinct pairs of adjacent and congruent sides.

11/13/ : Proving Quadrilateral Props Anatomy of a Kite Ends: Vertices where the congruent sides intersect.

11/13/ : Proving Quadrilateral Props Anatomy of a Kite The diagonal of a kite with its endpoints at the ends of the kite is the symmetry diagonal for the kite.

11/13/ : Proving Quadrilateral Props Properties of a Kite Theorem If a quadrilateral is a kite, then: a.The symmetry diagonal bisects the angles at the ends of the kite. b.Its diagonals are perpendicular.

11/13/ : Proving Quadrilateral Props Prove part a of the Properties of a Kite Theorem A B C D Given: ABCD is a kite.Prove: AC bisects  DAB and  DCB

11/13/ : Proving Quadrilateral Props Properties of a Parallelogram Theorem If a quadrilateral is a parallelogram, then: a)Each diagonal forms 2 congruent triangles. b)Both pairs of opposite angles are congruent. c)Each pair of opposite sides are congruent. d)Diagonals bisect each other. e)Consecutive angles are supplementary.

11/13/ : Proving Quadrilateral Props Properties of a Parallelogram Theorem Prove part a. Given: ABCD is a parallelogram. Prove:  ABC  CDA A B C D

11/13/ : Proving Quadrilateral Props Properties of a Rhombus Theorem If a quadrilateral is a rhombus, then: a.It is a parallelogram and a kite. b.Its diagonals are perpendicular. c.Its diagonals bisect opposite angles.

11/13/ : Proving Quadrilateral Props Properties of a Rectangle Theorem If a quadrilateral is a rectangle, then: a.It is a parallelogram. b.Its diagonals are congruent.

11/13/ : Proving Quadrilateral Props Properties of a Square Theorem If a quadrilateral is a square, then: a.It is a parallelogram, rectangle, rhombus and kite. b.Its diagonals are perpendicular, congruent, they bisect each other and they bisect the angles at opposite ends of the square.

11/13/ : Proving Quadrilateral Props Assignment Pages , # (all)