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## PowerPoint Slideshow about ' Construction' - hagop

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Construction 1a Construct a triangle (ASA)

Construction 1b Construct a triangle (SAS)

Construction 2 Construct the bisector of an angle

Construction 3 Construct the perpendicular bisector

of a line segment.

Construction 4 Construct the circumcircle of a triangle.

Construction 5 Construct the incircle of a triangle.

Construction 6 Divide the line segment [ab] into three

equal parts.

Construct the triangle PQR where |QR|=8cm, | PQR|=52o and |PRQ|=46o (A S A)

- At Q using a protractor mark and draw an angle of 52o.

- Draw a line segment [QR] 8cm in length. Name the points and mark the length.

- At R mark and draw an angle of 46o

- Mark the point of intersection of the two angles.

- This is the point P.

P

46°

52°

Quit

Q

R

|QR|=8cm

Menu

END OF CONSTRUCTION

Construct a triangle ABC where |AB| = 12cm, | BAC|=65o and |AC| = 9 cm (S A S)

USE MOUSE CLICKS TO VIEW CONSTRUCTION

- Draw a line segment 12cm in length. Name the points and mark the length.

- Use a protractor to draw a line at 65o to |AB|.

- Use a compass with A as centre and 9cm radius to draw an arc on this line.

- Mark the point of intersection C.

- Join C to B and complete labels.

C

|AC|=9cm

65°

Quit

A

b

|AB|=12cm

Menu

END OF CONSTRUCTION

Construct the bisector of an angle

- Draw the angle AOB.
- Using the vertex o as centre draw an arc to meet the arms of the angle at X and Y.
- Using X as centre and the same radius draw a new arc.
- Using Y as centre and the same radius draw an overlapping arc.
- Mark the point where the arcs meet.
- The bisector is the line from O to this point.

A

X

X

X

O

Quit

Y

Menu

B

END OF CONSTRUCTION

Construct the perpendicular bisector of a line segment

- Using A as centre and a radius greater than half |AB| draw an arc.

- Using B as centre and the same radius draw another arc.

- Draw a line through the points where the arcs cross.

- Draw the line segment

A

B

Quit

Menu

END OF CONSTRUCTION

Construct the circumcircle of a triangle

A

O

C

B

- Draw the triangle ABC

- Construct the perpendicular bisector of [AB]

Quit

- Construct the perpendicular bisector of [AC]

- The bisectors meet at O the circumcentre of the triangle

- Using O as centre and |OA| as radius construct the circumcircle of the triangle ABC

Menu

END OF CONSTRUCTION

Construct the incircle of a triangle

A

O

O

X

O

- Draw the triangle ABC
- Construct the bisector of angle ABC as shown.
- Construct the bisector of angle ACB as shown.
- The bisectors meet at point O, the incentre of the triangle
- Using O as centre construct the incircle of the triangle ABC

X

C

B

Quit

Menu

END OF CONSTRUCTION

Divide the line segment [AB] into three equal parts

- Draw the line segment [AB].
- Through A draw a line at an acute angle to [AB].
- On this line use circle arcs of the same radius to mark off three segments of equal length [AR], [RS] and [ST].
- Join T to B.
- Through S and R draw line segments parallel to [TB] to meet [AB] at D and C.
- Now |AC|=|CD|=|DB|

A

C

D

B

R

S

Quit

T

Menu

END OF CONSTRUCTION

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