Geometric Constructions- Angle Bisector

Unlock an effective teaching strategy for making connections in geometric constructions in this Teacher Perspectives video for educators.
Resource ID#: 211770 Type: Perspectives Video: Teaching Idea
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General Information

Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators educators
Keywords: geometric constructions, angle bisector, bisector, construction of angle bisector, geometric proof, proofs, constructions, reflexive property, congruent triangles, side side side, corresponding triangles
Instructional Component Type(s): Perspectives Video: Teaching Idea
Resource Collection: Perspective Videos: Math Teaching Ideas

Aligned Standards

This vetted resource aligns to concepts or skills in these benchmarks.

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Students will use segment constructions to verify and demonstrate the golden ratio. These proportional relationships connect the golden ratio to the ancient Greek ideal of beauty, balance, and harmony.
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Students will construct congruent segments on one ray of an angle and learn how to use a geometry set to create parallel lines to partition the other ray into a given ratio. The results are verified using corresponding angles and similar triangles.
Construction of the Bisector of a Segment

Students will construct the perpendicular bisector of a segment to verify the construction of a rhombus as a parallelogram. Similarities and differences between a segment bisector and perpendicular bisector are revealed.
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Students will use the construction of a perpendicular bisector to verify the Triangle Inequality Theorem. They will relate the radius of the compass needed to create intersecting arcs to the side-length conditions required for a triangle to exist.
Euler Line

Students will construct bisectors of segments to verify definitions and constructions of midpoints, medians, altitudes, the orthocenter, centroid, circumcenter, and the converse of the perpendicular bisector theorem, leading to the discovery of the Euler Line.
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Students will learn how to copy a given angle and use that skill to construct parallel lines. They will explore triangle congruence proofs and identify special angle pairs formed by parallel lines and transversals.
Circumscribed Circle of a Triangle and Nine-point Circle
Students will construct the circumscribed circle of a triangle and also identify the nine-point circle for a scalene triangle using compass and straightedge constructions. They will construct altitudes to locate the orthocenter and find the necessary midpoints to define the nine-point circle.

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