1.1 Lines in Designing a City
1.2 Angles in Measuring the Earth
1.3 Polygons and Polyhedra
1.4 Constructions
1.5 We can't go on like this
100
Who wrote the Elements and is known as the father of Geometry?
Euclid
100
What makes up an angle?
Two lines, line segments, or rays that intersect at a point.
100
The corners of a cube are points. What kind of geometric figure...
1)are its edges?
2)are its faces?
3)is the cube itself?
1) line segments
2)polygons/quadrilaterals
3)polyhedron
100
Constructions use which two of these tools?
Compass
Protractor
Ruler
Straightedge
Compass and Straightedge
100
Dido said she could buy a rectangular plot of land surrounded by a 900-yard-long cord. The land was in the shape of the figure below.
1)What is the perimeter (including the fourth side) of the figure below?
2)What is the area?
1)P=300+300+300+300= 4(300)=1200 yards
2)A=300*300=90,000
200
What is a plane?
A 2-dimensional figure that has no boundaries and is defined by 3 non-collinear points.
200
Measure the following angles:
1) ∠DAB
2) ∠ABE
3) ∠DCE
1) ∠DAB = 110°
2) ∠ABE = 150°
3) ∠DCE = 80°
200
The figure below is a transparent view of a cube
How many edges
1) meet at the corner of a cube?
2)does a cube have altogether?
How many faces
3)meet at the corner of a cube?
4)does a cube have altogether?
1)3
2)12
3)3
4)6
200
Bisect Line AB only using a compass and a straightedge
200
The following is another possible shape of Dido's land. If the cord is 900 yards long and in the shape of the figure below,
1) What is the perimeter of the property (including all 4 sides).
2) What is the area?
1) 900 = 200+200+x
x=500
The top side is 500 yards so
P=200+200+500+500=1400 yards
2) A=200*500=100,000 yards^2
300
Match the following numbers to letters
1) Line
2) Line Segment
3) Ray
A) A 1-dimensional figure that has one fixed endpoint but extends infinitely in the other direction
B) A 1-dimensional figure that has no depth but two fixed endpoints
C) An unmeasurable 1-dimensional figure that has no beginning or end
1)C
2)B
3)A
300
Give three ways to name the 70° angle in the figure below
∠A, ∠CAB, ∠BAC
300
The following pattern can be used to form a cube. Suppose it is cutout and folded to form a cube.
With which edge would each of the following edges come together?
1)JW
2)MN
3)LM
With which corner would the following corners come together?
4)R
5)W
1)PQ
2)NO
3)OP
4)T
5)Q and U
300
Bisect ∠DAB and ∠ABE. Draw the two bisectors long enough so that they meet at a point and label it F.
300
If Dido wants the most land, what should she make the dimensions of the rectangle? Assuming that the top three sides must add up to 900.
This is tricky and needs some experimenting to see what works best. This is just to challenge you and the test will not be this tricky. The most area will be when the length is 2x the width so that would be
900=x+2x+x=4x
900/4=x=225
225*450=101,250
So the rectangle would be 225 by 450