Step-by-StepConstructions

PerpendicularThrough A Point

(off a line)

EquilateralTriangle

What’s Wrongwith SSA?

Circumcenter

Incenter

A

P2P1

A2A1 P1

B

P4

P3

P2P1

P1 P2

P3

P4

P5

Centroid

P3

P1 P2

P4 PerpendicularBisector

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PerpendicularBisector

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1. adjust compass setting so that it is over half the length of given segment

2. construct an arc from each endpoint of the segment, P1 and P2, (arcs must intersect one another twice)

3. connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector).

The point where this perpendicular bisector intersects the original segment, C, is the midpoint

P1

Perpendicular Bisector

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1. adjust compass setting so that it is over half the length of given segment

2. construct an arc from each endpoint of the segment, P1 and P2, (arcs must intersect one another twice)

3. connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector).

The point where this perpendicular bisector intersects the original segment, C, is the midpoint

P2P1

Perpendicular Bisector

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1. adjust compass setting so that it is over half the length of given segment

2. construct an arc from each endpoint of the segment, P1 and P2, (arcs must intersect one another twice)

3. connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector).

The point where this perpendicular bisector intersects the original segment, C, is the midpoint

B

A

CP1 P2

Perpendicular Bisector

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1. adjust compass setting so that it is over half the length of given segment

2. construct an arc from each endpoint of the segment, P1 and P2, (arcs must intersect one another twice)

3. connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector).

The point where this perpendicular bisector intersects the original segment, C, is the midpoint

B

A

CP1 P2

Perpendicular Bisector

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PerpendicularThrough A

Point(off the line)

A

P1

P3P2

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Perpendicular Through a Point

1. adjust compass setting so that it is slightly more than the distance from the given point, P1, to the line

2. place the compass point on P1 and construct an arc that intersects the line in 2 places, P2 and P3 (if there's not enough room, you may need to extend the original line segment)

3. place the compass point on P2 and construct an arc on the opposite side of the segment from the given point, P1

4. repeat step #3 from other arc-line intersection, P3

5. connect the original point, P1, to the point where these two new arcs intersect, A, to create your perpendicular

P3P2

P1

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Perpendicular Through a Point

1. adjust compass setting so that it is slightly more than the distance from the given point, P1, to the line

2. place the compass point on P1 and construct an arc that intersects the line in 2 places, P2 and P3 (if there's not enough room, you may need to extend the original line segment)

3. place the compass point on P2 and construct an arc on the opposite side of the segment from the given point, P1

4. repeat step #3 from other arc-line intersection, P3

5. connect the original point, P1, to the point where these two new arcs intersect, A, to create your perpendicular

P1

P1

P3P2

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Perpendicular Through a Point

1. adjust compass setting so that it is slightly more than the distance from the given point, P1, to the line

2. place the compass point on P1 and construct an arc that intersects the line in 2 places, P2 and P3 (if there's not enough room, you may need to extend the original line segment)

3. place the compass point on P2 and construct an arc on the opposite side of the segment from the given point, P1

4. repeat step #3 from other arc-line intersection, P3

5. connect the original point, P1, to the point where these two new arcs intersect, A, to create your perpendicular

P2 P3

P1

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Perpendicular Through a Point

1. adjust compass setting so that it is slightly more than the distance from the given point, P1, to the line

2. place the compass point on P1 and construct an arc that intersects the line in 2 places, P2 and P3 (if there's not enough room, you may need to extend the original line segment)

3. place the compass point on P2 and construct an arc on the opposite side of the segment from the given point, P1

4. repeat step #3 from other arc-line intersection, P3

5. connect the original point, P1, to the point where these two new arcs intersect, A, to create your perpendicular

A

P1

P3P2

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Perpendicular Through a Point

1. adjust compass setting so that it is slightly more than the distance from the given point, P1, to the line

2. place the compass point on P1 and construct an arc that intersects the line in 2 places, P2 and P3 (if there's not enough room, you may need to extend the original line segment)

3. place the compass point on P2 and construct an arc on the opposite side of the segment from the given point, P1

4. repeat step #3 from other arc-line intersection, P3

5. connect the original point, P1, to the point where these two new arcs intersect, A, to create your perpendicular

A

P1

P3P2

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Equilateral Triangle

A

P2P1

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Equilateral Triangle

1. construct a segment2. place the compass tip on one

endpoint, P1, and adjust the pencil so that it reaches the other endpoint, P2. Construct an arc above the segment (using the length of the segment as the measure of your compass)

3. repeat step #2 from the other endpoint, P2 (keeping the compass measure the same) to locate A

4. connect the point where these two arcs intersect, A, to create an equilateral triangle

P2P1

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Equilateral Triangle

1. construct a segment2. place the compass tip on one

endpoint, P1, and adjust the pencil so that it reaches the other endpoint, P2. Construct an arc above the segment (using the length of the segment as the measure of your compass)

3. repeat step #2 from the other endpoint, P2 (keeping the compass measure the same) to locate A

4. connect the point where these two arcs intersect, A, to create an equilateral triangle

P1 P2

A

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Equilateral Triangle

1. construct a segment2. place the compass tip on one

endpoint, P1, and adjust the pencil so that it reaches the other endpoint, P2. Construct an arc above the segment (using the length of the segment as the measure of your compass)

3. repeat step #2 from the other endpoint, P2 (keeping the compass measure the same) to locate A

4. connect the point where these two arcs intersect, A, to create an equilateral triangle

A

P2P1

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Equilateral Triangle

1. construct a segment2. place the compass tip on one

endpoint, P1, and adjust the pencil so that it reaches the other endpoint, P2. Construct an arc above the segment (using the length of the segment as the measure of your compass)

3. repeat step #2 from the other endpoint, P2 (keeping the compass measure the same) to locate A

4. connect the point where these two arcs intersect, A, to create an equilateral triangle

A

P2P1

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What’s Wrong with

SSA?A2A1 P1

B

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What’s Wrong with SSA?

B

P1A

1. duplicate one angle at P1

2. duplicate one side, P1B 3. duplicate the next consecutive

side, BA

note, there are two possible intersections for the duplicated triangle P1BA1or2

Original Triangle

Duplication

P1

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What’s Wrong with SSA?

A P1

B

1. duplicate one angle at P1

2. duplicate one side, P1B 3. duplicate the next consecutive

side, BA

note, there are two possible intersections for the duplicated triangle P1BA1or2

Original Triangle

Duplication

B

P1

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What’s Wrong with SSA?

B

P1A

1. duplicate one angle at P1

2. duplicate one side, P1B 3. duplicate the next consecutive

side, BA

note, there are two possible intersections for the duplicated triangle P1BA1or2

Original Triangle

Duplication

A2A1 P1

B

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What’s Wrong with SSA?

A2A1 P1

B

1. duplicate one angle at P1

2. duplicate one side, P1B 3. duplicate the next consecutive

side, BA

note, there are two possible intersections for the duplicated triangle P1BA1or2

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CircumcenterP4

P3

P2P1

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Circumcenter

1. construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P4, is the circumcenter)

2. place the compass tip on the circumcenter, P4, and adjust the compass to a vertex, P1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

P4

P1 P2

P3

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Circumcenter

1. construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P4, is the circumcenter)

2. place the compass tip on the circumcenter, P4, and adjust the compass to a vertex, P1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

P4

P3

P2P1

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Circumcenter

1. construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P4, is the circumcenter)

2. place the compass tip on the circumcenter, P4, and adjust the compass to a vertex, P1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

P4

P3

P2P1

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IncenterP1 P2

P3

P4

P5

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Incenter

1. construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P4, is the incenter)

2. from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle)

3. place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

P4

P1 P2

P3

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Incenter

1. construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P4, is the incenter)

2. from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle)

3. place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

P5

P4

P3

P2P1

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Incenter

1. construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P4, is the incenter)

2. from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle)

3. place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

P1 P2

P3

P4

P5

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Incenter

1. construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P4, is the incenter)

2. from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle)

3. place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

P1 P2

P3

P4

P5

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CentroidB

A

C

P3

P1 P2

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Centroid

1. construct at least two perpendicular bisectors of the triangle, label the midpoints A and B

2. connect each midpoint, A and B, to its opposite vertex, P3 and P2 to form medians AP3 and BP2. The point of intersection of these two medians is the centroid, C

B

AP1 P2

P3

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Centroid

1. construct at least two perpendicular bisectors of the triangle, label the midpoints A and B

2. connect each midpoint, A and B, to its opposite vertex, P3 and P2 to form medians AP3 and BP2. The point of intersection of these two medians is the centroid, C

B

A

C

P3

P1 P2

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Centroid

1. construct at least two perpendicular bisectors of the triangle, label the midpoints A and B

2. connect each midpoint, A and B, to its opposite vertex, P3 and P2 to form medians AP3 and BP2. The point of intersection of these two medians is the centroid, C

B

A

C

P3

P1 P2