(Solved): CONSTRUCTION 2 Construct an Angle Congruent to a Civen Angle Construct an angle with vertex Q that i ...

CONSTRUCTION 2 Construct an Angle Congruent to a Civen Angle Construct an angle with vertex

that is congruent to

as shown. Procedure The construction procedure shows that

, and

. Therefore,

by the SSS property, so the corresponding angles

and

are congruent. 12.2 Constructing Geometric Figures * 633 CONSTRUCTION 3 Construct a Line Parallel to a Civen Une Given point

and line

as shown, construct a line through

that is parallel to L . CONSTRUCTION 4 Construct a Line Perpendicular to a Civen LineGiven line

and point

not on

as shown, construct a line through

that is perpendicular to

. Procedure Step 1: Construct an arc at

that intersects

at two points

and

. Step 2: With the coenpuss still

rodius AP, construct arcs at

ind 8 ind let

be their poier of inervection. Construct the line

; since

is a diaponal of thombus

, it is perperedicular so

. The construction of perpendicular lines has several applications: CHAPTER 12: Congruence, Constructions, and Similarity

SA Through a Polnt Not on the Glven Une Given line

and point

not on

as shown, construct a line through

that is perpendicular to

. Procedure Step 1: Construct an arc at

that imersects I at two points

and

. Step 2: With the compass still it radius

, construct ares at

and let

be their point of intersection. Construst the line

; since

is a diggonal of thembes ABPC, it is perpontlicufar 10 需. The construction of perpendicular lines has several applications: Nearest point

on a line / from a point

. The line through

thit is perpendicular to line / intersects

at the point

of

that ls ctosest to

. Whyl' I se the triangle inequalivy)

is called the foot of the perpendicular line from

, and

is called the distance from

to

. Point of reflection

of

across mirror line

, The point

on the perpendicular ko / through CONSTRUCTION 5 Construct the Line Perpendicular to a Given Line Through a Point on the Civen Line Given line

and point

on

as shown, construct the line throegh

peppendicular to

, Procedure Step 1: Construct two ares of equal radius centered at

; let

and

be their points of intersection with ? Step 2: Construct ares centered at

and

with a raliss gmiter thin AP? let

and

be their puins of intersectioe. Step 3: Construct line

, wince

is a diagoont it the thombus

and

is the midpeint of diagonal

, m passes through

and is perpendicular to

: that is,

is perpenterular sal. CONSTRUCTION 6 . Construct the Midpoint an