Congruency & Regularity
Are all rectangles regular? Why or why not?
No: regular means equal side lengths and equal angle measurements
(all squares are regular)
Perimeter of a square with side length 4.5 cm?
18 cm
Area of a rectangle with width 15 cm and length 22 cm?
330 cm2
Define and draw: "radius"
The distance from the center to the edge of a circle
Explain a pie (not pi) in terms of circumference and area.
circumference is crust
area is pie filling
Draw two triangles that ARE congruent.
Draw two more triangles that are NOT congruent.
Explain the difference.
Congruent = same side lengths and same angle measurements (exact same shape)
Not congruent = different side lengths or different angle measurements
Perimeter of a rectangle with length 8 cm and width 13 cm?
42 cm
Area of a rhombus with side lengths all 6 cm and height 5 cm?
30 cm2
Define and draw: "diameter"
The distance from edge to edge, through the center, in a circle
Give a strategy to help remember that 2(pi)(r) is circumference and pi(r)(r) is area
r squared is usually bigger than 2r (make a table of values to see why) and area is usually bigger than circumference
Draw two congruent triangles. Label their vertices. Then, write one congruency statement for sides and one congruency statement for angles.
Example: side AB is congruent to side DE and angle A is congruent to angle D
use congruency symbol!
Perimeter of an isosceles triangle with congruent sides of length 6.5 cm and other side of length 8 cm?
21 cm
Area of a parallelogram with base 8 cm, side lengths 20 cm, and height 18 cm?
144 cm2
What is the relationship between radius and diameter, and WHY?
Radius is half diameter
Diameter is twice radius
The half/twice relationship is because every point on a circle is equidistant from the center
What is the circumference of a circle with a radius of 9 inches?
2(pi)(9) = 56.55 inches
Congruent shapes stay congruent if one of them is... (name the following verbs as true or false): rotated, stretched, flipped, scaled, folded
True: rotated, flipped
False: stretched, scaled, folded
Perimeter of an isosceles trapezoid with bottom side 3 cm, top side twice as long as bottom side, and sides 5/6 as long as top side?
19 cm
Area of a scalene triangle with side lengths 3, 4, and 5 cm?
6 cm2
Define, draw, and give a real-world example of: "circumference"
The distance around the edge of a circle
2 pi r
What is the area of a circle with diameter 12 inches?
Diameter 12 --> radius 6
pi(6 squared) = pi(36) = 113.1 square inches
Draw a regular octagon and all of its lines of symmetry.
8 sides and 8 lines of symmetry
Perimeter of a house shape with roof length 7 cm, wall length 10 cm, and base length 12 cm?
46 cm
Area of an isosceles trapezoid with height 5 cm, bottom side 20 cm, and top side 12 cm?
80 cm2
Define, draw, and give a real-world example of: "area" (for circles)
How many square units fill the circle
pi r squared
Patrick likes pizza. Chris likes crust. Each of them has enough money for either two 12-inch medium pizzas OR one 18-inch large pizza. Which option should Patrick choose? Which option should Chris choose? (Note: pizza measurements refer to diameter).
Patrick should choose the one 18-inch large pizza (for more area).
Chris should choose the two 12-inch medium pizzas (for more circumference).