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Geometry Terms October 2007 Concentric • Concentric circles share the same centre Converse • Converse means the "if" and "then" parts of a sentence are switched. For example, "If two numbers are both even, then their sum is even" is a true statement. The converse would be "If the sum of two numbers is even, then the numbers are even," which is not a true statement. Write the converse of the statement. • If two chords on a circle are equidistant from the centre of the circle, then they are congruent. • If two chords of a circle are congruent, then they are equidistant from the centre of the circle • If a statement and its converse are both true, then they can be written using iff, which means “if and only if” • For example: the preceding example can be written as “Two chords on a circle are equidistant from the centre of a circle iff they are the same length.” Or: “Two chords of a circle are the same length iff they are equidistant from the centre of a circle.” Properties of Chords • Chords that are equidistant from the centre of a circle are equal in length • Chords that are equal in length are equidistant from the centre of a circle • The perpendicular bisectors of two chords pass through the center of the circle Proving triangles congruent •Side - Angle – Side •If two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. Side – Side - Side •If three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. Angle – Angle - Angle •If two angles and one side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Angle – Angle - Side •If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, the two triangles are congruent. Right angle – Hypotenuse - Side •If two right triangles have a hypotenuse and a corresponding congruent leg then the triangles are congruent. Terms to remember •Isosceles Triangle •Vertical angles •Corresponding angles •Transversal •Alternate Interior angles •Supplementary angles •Co-interior angles Answers 1. a)SSS b) AAS c) Not d) Not e) ASA f) ASA