Construct a perpendicular line (Tutorial)

Learning Objectives Construct a line perpendicular to a given line through a point on the line using only a compass and straightedge. Construct a line perpendicular to a given line from a point not on the line using only a compass and straightedge. Construct the perpendicular bisector of a given line segment. Define and correctly use the terms: perpendicular, bisector, compass, straightedge, and arc. Justify the validity of a perpendicular construction using principles of congruent triangles (SSS, SAS). Apply perpendicular line constructions to find the altitude of a triangle from a given vertex. Ever wonder how architects ensure every corner in a skyscraper is a perfect 90-degree angle? It all starts with the fundamental geometric skill you're about to learn! 📐 This...

TermDefinitionExample Perpendicular LinesTwo lines that intersect to form a right angle (90°). The symbol for perpendicular is ⊥.If line AB ⊥ line CD, the angle formed at their intersection is 90°. CompassA geometric tool used to draw circles or arcs of a fixed radius. It is essential for transferring equal lengths.Setting the compass to a 5 cm radius allows you to draw a circle where every point on the circumference is exactly 5 cm from the center. StraightedgeA tool used for drawing straight lines. Unlike a ruler, a straightedge has no measurement markings.Using a straightedge to connect two points, A and B, creates the line segment AB. Line SegmentA part of a line that is bounded by two distinct endpoints.The edge of a desk is a physical representation of a line segment. Perpendicular...

Equidistant Points Theorem If two points are each equidistant from the endpoints of a segment, then the line containing them is the perpendicular bisector of the segment. This is the foundational principle for constructing perpendicular bisectors. If you have a segment AB, and you find two points P and Q such that PA = PB and QA = QB, then the line PQ is the perpendicular bisector of AB. Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to the three corresponding sides of another triangle (e.g., \triangle ABC \cong \triangle DEF if AB=DE, BC=EF, and AC=DF), then the two triangles are congruent. We use this postulate to prove that our constructions are valid. By creating triangles with sides of equal length (using the compass), we can prov...