Chapter 6 Lesson 2Chapter 6 Lesson 2Chapter 6 Lesson 2Chapter 6 Lesson 2Objective:Objective: To use relationships To use relationships
among diagonals, angles and sides of among diagonals, angles and sides of parallelograms.parallelograms.
Properties of ParallelogramsTheorem 6-1
Opposite sides of a parallelogram are congruent.
Angles of a polygon that share a side are consecutive angles. A parallelogram has opposite sides parallel. Its consecutive angles are same-side interior angles so they are supplementary. In ABCD, consecutive angles B and C are supplementary, as are consecutive angles C and D.
Example 1: Using Consecutive Angles
Find m S in RSTW .
R and S are consecutive angles of a parallelogram. They are supplementary.
Example 2: Using Consecutive Angles
Find m O in KMOQ .
K M
OQ35°
Q and O are consecutive angles of a parallelogram. They are supplementary.
180 OmQm18035 Om
145Om
Theorem 6-2
Opposite angles of a parallelogram are congruent.
Example 3: Using Algebra
Find the value of x in PQRS. Then find QR and PS.
Example 4: Using Algebra
Find the value of y in parallelogram EFGH.
GmEm 37346 yy
333 y11y
Theorem 6-3
The diagonals of a parallelogram bisect each other.
Example 5: Using AlgebraSolve a system of linear equations to find the values of x and y in ABCD. Then find AE, EC, BE, and
ED.
Step 1: Write equations.
yx 1xy 273 Diagonals
bisect each other.
Step 2: Solve for a variable and Substitute xx 27)1(3
Step 3: Solve for variables
xx 2733 xx 243
4x
yx 1y14
y5
Example 6: Using Algebra
Find the values of a and b.
Step 1: Write equations.
2ba8210 ab
Diagonals bisect each other.
Step 2: Solve for a variable and Substitute 8)2(210 bb
Step 3: Solve for variables
84210 bb4210 bb
14b
2ba214a
16a
Theorem 6-4If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off
congruent segments on every transversal.
DFBD
Assignment
Pg. 297-300#1-
22(evens); 24-37; 39; 52
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