1 / 13

4.5: Proving Quadrilateral Properties

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. B. A. C. D.

Download Presentation

4.5: Proving Quadrilateral Properties

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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. 4.5: Proving Quadrilateral Props

  2. B A C D • 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? • 30° • 45 • 60 • 90 • Cannot be determined from the given information 4.5: Proving Quadrilateral Props

  3. Kites • Defn: A quadrilateral is a kite iff it has 2 distinct pairs of adjacent and congruent sides. 4.5: Proving Quadrilateral Props

  4. Anatomy of a Kite Ends: Vertices where the congruent sides intersect. 4.5: Proving Quadrilateral Props

  5. 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. 4.5: Proving Quadrilateral Props

  6. Properties of a Kite Theorem • If a quadrilateral is a kite, then: • The symmetry diagonal bisects the angles at the ends of the kite. • Its diagonals are perpendicular. 4.5: Proving Quadrilateral Props

  7. Prove part a of the Properties of a Kite Theorem Given: ABCD is a kite. Prove: AC bisects DAB and DCB D A C B 4.5: Proving Quadrilateral Props

  8. Properties of a Parallelogram Theorem • If a quadrilateral is a parallelogram, then: • Each diagonal forms 2 congruent triangles. • Both pairs of opposite angles are congruent. • Each pair of opposite sides are congruent. • Diagonals bisect each other. • Consecutive angles are supplementary. 4.5: Proving Quadrilateral Props

  9. Properties of a Parallelogram Theorem • Prove part a. • Given: ABCD is a parallelogram. • Prove: ABC CDA C B A D 4.5: Proving Quadrilateral Props

  10. Properties of a Rhombus Theorem • If a quadrilateral is a rhombus, then: • It is a parallelogram and a kite. • Its diagonals are perpendicular. • Its diagonals bisect opposite angles. 4.5: Proving Quadrilateral Props

  11. Properties of a Rectangle Theorem • If a quadrilateral is a rectangle, then: • It is a parallelogram. • Its diagonals are congruent. 4.5: Proving Quadrilateral Props

  12. Properties of a Square Theorem • If a quadrilateral is a square, then: • It is a parallelogram, rectangle, rhombus and kite. • Its diagonals are perpendicular, congruent, they bisect each other and they bisect the angles at opposite ends of the square. 4.5: Proving Quadrilateral Props

  13. Assignment • Pages 248-249, # 42-66 (all) 4.5: Proving Quadrilateral Props

More Related