6.3 Properties of Parallelograms Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon n 3 4 5 6 7 8 9 n-2 1 2 3 4 5 6 7 Sum of angles 180 degrees 720 degrees

6.3 Properties of Parallelograms

• Goal #1: • How to use properties of parallelograms to solve problems in geometry.

• Goal #2: • How to use properties of parallelograms to solve real life problems.

6.3 Properties of Parallelograms

Power Sta ndar d #8 Understand the properties, characteristics, and notation of geometric figures/solids to determine how they relate to one another. (1.3.2) [1.2, 6.

1-6.3, 6.

5, 6.6]

Parallelogram

• A parallelogram is a quadrilateral whose opposite sides are parallel.

Lesson Investigation

Part A - Instructions • In pairs, use a straightedge to draw two parallel segments on a piece of patty paper. Then draw two other parallel segments to form a parallelogram. • Place a second piece of patty paper over the first and copy the parallelogram onto the second. • By moving the copies around, what conjectures can you make about the properties of parallelograms. • You have ten minutes!!! Part A – Guiding Questions • How do the lengths of the opposite sides compare?

• How do the sizes of the opposite angles compare?

• How do the sizes of consecutive angles compare?

Parallelogram

Part A – Guiding Questions • How do the lengths of the opposite sides compare?

• How do the sizes of the opposite angles compare?

• How do the sizes of consecutive angles compare?

Lesson Investigation

Part B – Instructions • Draw or fold the two diagonals of the parallelogram.

• Place a dot at their intersection.

• You have five minutes!!!

Part B - Guiding Questions • How do the segments of each diagonal compare?

• What can be said about the intersection of the diagonals?

• How many congruent triangles are formed within the parallelogram?

Parallelogram

Part B - Guiding Questions • How do the segments of each diagonal compare?

• What can be said about the intersection of the diagonals?

• How many congruent triangles are formed within the parallelogram?

Properties of Parallelograms

• THM 6.3: The opposite sides of a parallelogram are congruent.

• THM 6.4: The opposite angles of a parallelogram are congruent.

Properties of Parallelograms

• THM 6.5: The consecutive interior angles of a parallelogram are supplementary. 1 2

m m

2 180 THM 6.6: The diagonals of a parallelogram bisect each other.

Find , ,  ,  if

PQRS

is a ogram and  A.

SR

B.

ST

 

QT

  5 3 C.

m



PQR

 70 D.

m



QRS

 110 S , P 110  110 5 3 T 3 5 110 R 70 Q

Using Parallelograms to solve Real life problems

• The San Francisco Bay Bridge, like many bridges, uses parallelograms in its structural design. • Engineers use properties of parallelograms to build and repair bridges.

The framework for a railroad bridge is shown below.

You know only that ____ ____ ____ ED BC , AB ____ EF , and m  PER  130  .

130  A. Are you given enough info to verify that EQ = QB?

Yes!

 B. What are the measures of ERB and RBP?

50 130

Assignment!!!

• Pg. 283 • 11-23 odd, • 27b-36 even, • 42, 44.