Proofs in Geometry

A series of free, online High School Geometry Video Lessons.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we willl learn

  • how to use CPCTC
  • how to use two column proofs
  • how to use flowchart proofs
  • how to use special isosceles triangle properties




CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

How to use the principle that corresponding parts of congruent triangles are congruent, or CPCTC.

How do we Use CPCTC?



Two Column Proofs

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.

How to organize a two column proof.

A brief lesson and practice on drawing diagrams and completing two column proofs from word problems



Flowchart Proofs

Flowchart proofs are organized with boxes and arrows; each "statement" is inside the box and each "reason" is underneath each box. Each statement in a proof allows another subsequent statement to be made. In flowchart proofs, this progression is shown through arrows. Flowchart proofs are useful because it allows the reader to see how each statement leads to the conclusion.

How to outline a flowchart proof.

Using flowcharts in proofs for Geometry



Special Isosceles Triangle Properties

In isosceles (and equilateral) triangles, a segment drawn from the vertex angle to the opposite side is the altitude, angle bisector and median. Isosceles triangle properties are used in many proofs and problems where the student must realize that, for example, an altitude is also a median or an angle bisector to find a missing side or angle.

 How to identify a segment from the vertex angle in an isosceles triangle to the opposite side.




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