0
6.3 Proving Quadrilaterals are Parallelograms <ul><li>Objective: </li></ul><ul><li>Prove that a quadrilateral is a paralle...
<ul><li>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.  </li...
Theorem <ul><li>If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogr...
Theorem <ul><li>If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral ...
Theorem <ul><li>If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.  </li></ul>
Proof <ul><li>Prove Theorem 6.6 - If both pairs of opposite sides are   , then the quadrilateral is a parallelogram. </li...
Proof <ul><li>AB    CD and AD    CB </li></ul><ul><li>AC    AC </li></ul><ul><li>∆ ABC    ∆CDA </li></ul><ul><li><BAC ...
Theorem <ul><li>If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a p...
Summary - How can we prove quadrilaterals are parallelograms? <ul><li>Show that both pairs of opposite sides are || </li><...
Using Coordinate Geometry <ul><li>When a figure is in the coordinate plane, you can use the Distance Formula to prove that...
Homework:   p. 342 10-24 evens
Upcoming SlideShare
Loading in...5
×

Geom 6point3 97

5,021

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
5,021
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
41
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Geom 6point3 97"

  1. 1. 6.3 Proving Quadrilaterals are Parallelograms <ul><li>Objective: </li></ul><ul><li>Prove that a quadrilateral is a parallelogram </li></ul><ul><li>Use coordinate geometry with parallelograms. </li></ul>
  2. 2. <ul><li>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. </li></ul>Theorem
  3. 3. Theorem <ul><li>If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. </li></ul>
  4. 4. Theorem <ul><li>If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. </li></ul>x˚ 180 - x˚ x˚
  5. 5. Theorem <ul><li>If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. </li></ul>
  6. 6. Proof <ul><li>Prove Theorem 6.6 - If both pairs of opposite sides are  , then the quadrilateral is a parallelogram. </li></ul><ul><li>Given: AB  CD and AD  CB </li></ul><ul><li>Prove: ABCD is a parallelogram </li></ul>A B C D
  7. 7. Proof <ul><li>AB  CD and AD  CB </li></ul><ul><li>AC  AC </li></ul><ul><li>∆ ABC  ∆CDA </li></ul><ul><li><BAC  <DCA, <DAC  <BCA </li></ul><ul><li>AB || CD, AD || CB </li></ul><ul><li>ABCD is a parallelogram. </li></ul><ul><li>Given </li></ul><ul><li>Reflexive </li></ul><ul><li>SSS </li></ul><ul><li>CPCTC </li></ul><ul><li>Alternate Interior Angles Converse </li></ul><ul><li>Definition of a parallelogram </li></ul>A B C D
  8. 8. Theorem <ul><li>If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram </li></ul>
  9. 9. Summary - How can we prove quadrilaterals are parallelograms? <ul><li>Show that both pairs of opposite sides are || </li></ul><ul><li>Show that both pairs of opposite sides are  </li></ul><ul><li>Show that both pairs of opposite angles are  </li></ul><ul><li>Show that one angle is supplementary to both consecutive angles </li></ul><ul><li>Show that the diagonals bisect each other </li></ul><ul><li>Show that one pair of opposite sides are  and || </li></ul>
  10. 10. Using Coordinate Geometry <ul><li>When a figure is in the coordinate plane, you can use the Distance Formula to prove that the sides are congruent and you can use the slope formula to prove that sides are parallel. </li></ul><ul><li>Go through Example 4 on p. 341 </li></ul><ul><li>Do p. 342 1-8 </li></ul>
  11. 11. Homework: p. 342 10-24 evens
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×