Measuring Height with Triangles and Mirrors

Reflect for a moment on how to measure tall objects with mirrors and mathematics.
Resource ID#: 130636 Type: Perspectives Video: Teaching Idea
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General Information

Subject(s): Mathematics
Grade Level(s): 8, 9, 10, 11, 12
Intended Audience: Educators educators
Keywords: angle of incidence, triangles, scale, congruent, congruent triangles, similar, similar triangles, scale factor, DeLand High School
Instructional Component Type(s): Perspectives Video: Teaching Idea
Resource Collection: CPALMS Perspectives Videos - General

Aligned Standards

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

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Introducing Construction Tools and Basic Geometric Constructions

Students will learn to use basic geometric construction tools to copy a segment and an angle, then apply these skills repeatedly to construct a rhombus. The definition of a parallelogram is verified.
The Golden Ratio

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.
Parallel Lines and Partitions

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.
Related Constructions to the Perpendicular Bisector

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.
Copying an Angle and Parallel Lines
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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