Given and Prove

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 1 of 63.

So far you have found sizes. A proof answers a different question: not how big something is, but why a fact must be true. Every proof starts from the given, the facts you are told, and ends at the statement you were asked to prove.

Much of the given is drawn on the figure as marks. Matching tick marks say sides are equal, matching arcs say angles are equal, a small square says an angle is 90°, and matching arrowheads (chevrons) say lines are parallel. Some facts are written in words instead, like "M is the midpoint of AB". Both kinds count the same.

$A kite ABCD: single ticks on AB and AD, double ticks on CB and CD, and the diagonal AC$

In this kite the single ticks give AB = AD and the double ticks give CB = CD. Nothing says AB = CB: different marks mean the figure promises nothing about that pair, however alike they look.