DO NOWSketch each figure.1)CD2)GH3)AB4)Line m5)Acute ABC6)XY II ST

Basic Constructions

GeometryWeek 3 of 9

Unit 1: Logic & Reasoning

9/9 & 9/109/9 & 9/10

Standards & ObjectiveStandard 16.0Students perform basic constructions with a straightedge and compass, such as angle bisectors and perpendicular bisectors.

Objective:• Use a compass and a straightedge to construct congruent

segments and congruent angles• Use a compass and a straightedge to bisect segments and

angles

Example: Constructing Congruent SegmentsConstruct a segment congruent

to a given segmentGiven: ABConstruct: CD so that CD = ABStep 1: Draw a ray with

endpoint CStep 2: Open the compass to

the length of ABStep 3: With the same compass

setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.

Practice: Constructing Congruent Segments

1. Construct XY congruent to AB.

2. Construct VW so that VW = 2AB

A ● ● B 2 inches

Example: Constructing Congruent AnglesConstruct an angle congruent to a

given angle.Given: AConstruct: S so that S = AStep 1: Draw a ray with endpoint SStep 2: With the compass point on

point A, draw an arc that intersects the sides of A. Label the points of intersection B and C.

Step 3: With the same compass setting, put the compass point on point S. Draw an arc and label its point of intersection with the ray as R.

Step 4: Open the compass to the length BC. Keeping the same compass setting, put the compass point on R. Draw an arc to locate point T.

Step 5: Draw ST

Practice: Constructing Congruent Angles

Construct D so that D = C

C

Constructing the Perpendicular BisectorConstruct the perpendicular bisector of

a segment.Given: ABConstruct: XY so that XY AB at the

midpoint M of ABStep 1: Put the compass point on point

A and draw a long arc as shown. Be sure the opening is greater than ⅟2

AB.Step 2: With the same compass

setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect as X and Y.

Step 3: Draw XY. The point of intersection of AB and XY is M, the midpoint of AB.

XY AB at the midpoint of AB, so that XY is the perpendicular bisector of AB.

Draw ST. Construct its perpendicular bisector.

Practice: Constructing the Perpendicular Bisector

Construct the perpendicular bisector of AB

● ●

A B

Finding Angle MeasuresAngle Bisector: a ray that divides an

angle into two congruent angles.KN bisects JKL so that m JKN = 5x-

25 and m NKL = 3x+5. Solve for x and find m JKN.

m JKN = m NKL5x – 25 = 3x + 55x = 3x + 302x = 30X = 15m JKN = 5x – 25 = 5(15) – 25 = 50m JKN = 50

Definition of Angle BisectorSubstituteAdd 25 to each sideSubtract 3x from each sideDivide each side by 2Substitute 15 for x

Practice: Finding Angle Measures

GH bisects FGI.a) Solve for x b) Find m HGIc) Find m FGI

F

H

IG

(3x -3)

(4x – 14)

Constructing the Angle BisectorConstruct the bisector of an angleGiven: AConstruct: AX, the bisector of AStep 1: Put the compass point on

vertex A. Draw an arc that intersects the sides of A. Label the points of intersection B and C.

Step 2: Put the compass point on point C and draw an arc. With the same compass setting, draw an arc using point B. Be sure the arcs intersect. Label the point where the two arcs intersect as X.

Step 3: Draw AX.AX is the bisector of CAB.