Download Geo (H) 6.2 Parallelograms.notebook

Geo (H) 6.2 Parallelograms.notebook
December 03, 2014
6.2 Parallelograms
Objecves:
1. You will be able to recognize & apply properes of the sides and angles of parallelograms. 2. You will be able to recognize & apply properes of the diagonals of parallelograms. 1. WALKWAY A walkway is made by adjoining four parallelograms as shown.
Are the end segments a and e parallel to each other? Explain.
Yes. Opposite sides of a
parallelogram are parallel and the
parallel property is transitive.
2. DISTANCE Four friends live at the four corners of a block shaped like a parallelogram. Gracie lives 3 miles away from Kenny. How far apart do Teresa and Travis live from each other?
Since opposite sides in a parallelogram are
congruent, Travis and Teresa live 3 miles apart as well. 3. SOCCER Four soccer players are located at the corners of a parallelogram. Two
of the players in opposite corners are the goalies. In order for goalie A to be able to see the three others, she must be able to see a certain angle x in her field of vision. What angle does the other goalie have to be able to see in order to keep an eye on the other three players?
Goalie B would have to have the same view as Goalie A since opposite angles in a parallelogram are congruent so
Goalie B would have a view of xo.
Geo (H) 6.2 Parallelograms.notebook
December 03, 2014
4. VENN DIAGRAMS Make a Venn diagram showing the relaonship between squares, rectangles, and parallelograms.
5. SKYSCRAPERS On vacaon, Tony’s family took a helicopter tour of the city. The pilot said the newest building in the city was the building with this top view. He
told Tony that the exterior angle by the front entrance is 72°. Tony wanted to know more about the building, so he drew this diagram and used his geometry skills to learn a few more things. The front entrance is next to vertex B.
What are the measures of the four
angles of the parallelogram?
72, 72, 108, 108
How many pairs of congruent
triangles are there in the figure? What are they?
Geo (H) 6.2 Parallelograms.notebook
December 03, 2014
ALGEBRA Find the value of each variable. Give the jusficaon for each.
Opposite Sides Congruent
2b ­ 1 = b + 3
b = 4
Opposite Sides Congruent
2a = 3a ­ 5
a = 5
Opposite Angles Congruent
y = 44
Consecutive Angles Supplementary
x = 136
Diagonals bisect each other.
x ­ 2 = 19
x = 21
Diagonals bisect each other.
y + 1 = 26
y = 25
Geo (H) 6.2 Parallelograms.notebook
December 03, 2014
Opposite Sides Congruent
a + 14 = 6a + 4
a = 2
Opposite Sides Congruent
9b + 8 = 10b + 1
b = 7
Consecutive Angles Supplementary
x + 8 + 3x = 180
x = 43
Opposite Angles Congruent
3(43) = y + 9
129 = y + 9
y = 120
Diagonals bisect each other.
4x ­ 2 = x + 10
x = 4
Diagonals bisect each other.
y + 5 = 3y ­ 1
y = 3