Statements and Reasons

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 2 of 63.

A proof is written as a list of statements, each with a reason. A reason is a given fact, or a rule you already know. Some rules need earlier lines: the rule only applies because something above it is true, so the line names the lines it uses.

$Triangle KLN with ticks on KL and KN$

Statement	Reason
1. KL = KN	Given (the ticks)
2. ∠KLN = ∠KNL	Base angles of an isosceles triangle, using line 1

Line 1 comes straight from the marks. Line 2 uses a rule from the Angles section: equal sides face equal angles. That rule needs two equal sides, so line 2 points back to line 1. Another rule you will use often is All right angles are equal: every right angle is 90°, so two of them are equal once you have a line saying each is a right angle.

Challenge

Two right angles are marked with squares. The three statements are written; give each one its reason, and pick the earlier lines a reason uses. Then press Check.

On this board, tap a line, pick its reason from the menu, and tap the lines it cites.

Try it yourself

$Write the proof$