Construction Basics
Circles
Equidistance
Triangles and More
Constructions
100
What two tools are specifically allowed on this assessment for geometric constructions?
Straightedge and compass
100
A circle is drawn with center P and radius 7 cm. How far is every point on the circle from P?
7 cm
100
Define equilateral.
all equal (congruent) sides
100
A triangle has three congruent sides. What type of triangle is it?
Equilateral
100
When constructing the perpendicular bisector of AB, where should the compass be centered first?
At one endpoint of the segment
200
A point is on a circle centered at A. What can you say about the line segment formed between this point and point A?
It is equal to the radius
200
Point E lies on the perpendicular bisector of segment AB. Which is true?
A. EA > EB
B. EA < EB
C. EA = EB
D. Nothing can be determined
C. EA = EB
200
A triangle has two congruent sides. What type of triangle is it?
Isosceles
200
Two congruent circles are drawn centered at A and B. Their intersection points are C and D. What can you conclude about AC, BC, AD, and BD?
All four segments have the same length
300
Circle A and Circle B have the same radius. Point C lies on both circles. What can you conclude about AC and BC?
AC = BC
300
Point P is equidistant from A and B. If PA = 9 cm, what is PB?
PB = 9
300
If AB=AC, which type of triangle is △ABC
Isosceles
300
What construction creates the perpendicular bisector of a segment?
Draw congruent arcs/circles centered at the endpoints of the segment, then draw the line through their intersection points.
400
What construction does this image show?
Perpendicular Bisector
400
Circle A and Circle B have the same radius. What can you conclude about their sizes?
Their radii are congruent/equal in length.
400
A point is equidistant from the endpoints of a segment. Where must that point lie?
On the perpendicular bisector of the segment.
400
Give all four ways to name this angle.
angle A
angle CAB
angle BAC
angle 1
400
If two congruent circles are centered at the endpoints of AB and intersect at C and D, what can you say about C and D?
Both C and D are equidistant from A and B, so line CD is the perpendicular bisector of AB
500
What construction does this image show?
Angle Bisector
500
Give a complete definition of a circle.
A set of all points that are the same distance from a center.
500
A construction creates AB=BC=CD=DA. What can you conclude about quadrilateral ABCD? (What type of quadrilateral is ABCD?)
It has four congruent sides. (It forms a rhombus)
500
Three circles have centers A, B, and C. The construction shows that AB = AC. What type of triangle is △ABC?
Isosceles triangle
500
CONSTRUCTION CHALLENGE:
Construct the perpendicular bisector of segment AB. Then explain two facts that are true about the resulting line.
- It is perpendicular to AB.
- It passes through the midpoint of AB.
- Every point on it is equidistant from A and B.