1 / 14

Section 5.5

Section 5.5. Properties of Quadrilaterals. Properties of Parallelograms. Opposite sides are parallel ( DC ll AB, AD ll BC ) Opposite sides are congruent ( DA CB, DC AB ) Opposite angles are congruent (<DAB <DCB, <ABC <ADC)

kirby-robbins
Download Presentation

Section 5.5

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. Section 5.5 Properties of Quadrilaterals

  2. Properties of Parallelograms • Opposite sides are parallel ( DC ll AB, AD ll BC ) • Opposite sides are congruent ( DA CB, DC AB ) • Opposite angles are congruent (<DAB <DCB, <ABC <ADC) • Diagonals bisect each other (DB bis. AC, AC bis. DB) • Consecutive angles are supplementary(<DAB suppl. <ADC, etc.) • Diagonals form 2 congruent triangles ( ABC CDA, DCB BAD)

  3. Properties of A Rectangle • All properties of a parallelogram apply • All angles are right angles and . • Diagonals are ( ) B A C D

  4. Properties of a kite • Two disjoint pairs of consecutive sides are • Diagonals are • One diagonal is the bisector of the other • One of the diagonals bisect a pair of opposite <‘s • One pair of opposite <‘s are A D B C

  5. Properties of a Rhombus • Parallelogram Properties • Kite Properties • All sides are congruent • Diagonals bisect the angles • Diagonals are perpendicular bisectorsof each other • Diagonals divide the rhombus into 4 congruent rt. Triangles

  6. Properties of squares • Rectangle Properties • Rhombus Properties • Diagonals form 4 isos. right triangles

  7. Properties of trapezoids • Exactly one pair of sides parallel

  8. Properties of isosceles trapezoids • Legs are congruent • Bases are parallel • Lower base angles are congruent • Upper base angles are congruent • Diagonals are congruent • Lower base angles are suppl. to upper base angles

  9. Always, sometimes, never The diagonals of a rectangle are congruent Every square is a rectangle Every quadrilateral is a trapezoid In a trap. opp angles are congruent A rhombus is a rectangle An isos. trap is parallelogram Consecutive angles of a square are congruent Rhombuses are parallelograms Squares have only one right angle No trapezoid is a rectangle An isosceles trapezoid has no parallel lines Always Always Sometimes Never Sometimes Never Always Always Never Always Never Practice Problems

  10. C Sample problems Given: Triangle ACE is isos. With base AE CD CB AG FE BD GF Prove: BGFD is a parallelogram B D E A G F Statements Reasons tri. ACE is isos. w/ base AE CD CB AG FE BD GF 1. Given 2. Given 3. Given 4. Given 5. <A <E 5. If isos, then <‘s 6. CA CE 6. If <‘s, then sides 7. BA DE 7. Subtraction 8. Tri. BAG Tri. DEF 8. SAS(3,5,7) 9. BG DF 9. CPCTC 10. BGDF is a parallelogram 10. If opp. sides are then figure is a parallelogram

  11. Sample problem #2 Given: ABCD is a rhombus E Prove: AC is perp. DB

  12. Sample Problem #2 E Statement Reason 1. ABCD is a rhombus 2. AD DC 3. DE DE 4. AE CE 5. Tri. ADE and Tri. CDE 6. <AED <CED 7. <AED and <CED are rt <s 8. AC DB 1. Given 2. In a rhombus opp. Sides are 3. Reflexive 4. In a parallelogram diag. bisect each other 5. SSS(2,3,4) 6. CPCTC 7. If 2 <s are and suppl. They are rt. <s. 8. Rt <s are formed by perp. lines

  13. Works Cited "Quickie Math." Quickie Math , n.d. Web. 19 Jan 2011. <library.thinkquest.org/C006354/11_1.html>. Rhoad, Richard, George Miluaskas, and Robert Whipple. Geometry for Enjoyment and Challenge. New Edition ed. Boston: McDougal Littell, 1997. Print. “Rhombus problems." analyze math. A Dendane , 5 November 2010. Web. 19 Jan 2011. <http://www.analyzemath.com/Geometry/rhombus _problems.html>.

More Related