Geometry Unit 4 - Congruent Figures

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Definition of Congruent Polygons

Definition of Congruent Polygons

Polygons are congruent if and only if their corresponding parts are congruent.

(When you name congruent polygons, you must list corresponding vertices in the same order.)

Definition of Congruent Triangles

Two triangles are congruent if and only if the corresponding parts of the two triangles are congruent. This definition is conventionally stated as, “corresponding parts of congruent triangles are congruent” and conventionally abbreviated as CPCTC.

Definition of Polygons

A figure with 3 or more slides

FIND A PIC

What angle is opposite segment __

FAP

What angle is adjacent to <___

Hypotenuse

The angle opposite the right angle is called the

fap

Is this triangle isosceles? Answer yes or no.

The Isosceles Triangle Theorem

If two sides of a triangle are congruent then the angles opposite those sides are congruent.

The Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent then the sides opposite those angles are congruent.

Unnamed Theorem

If a line bisects the vertex angle of an isosceles triangle then the line is also the perpendicular bisector of the base.

A Corollary to the Converse of the Isosceles Triangle Theorem

If a triangle is equiangular then the triangle is equilateral.

A Corollary to the Isosceles Triangle Theorem

If a triangle is equilateral then the triangle is equiangular.

The Triangle Angle-Sum Theorem

If a polygon is a triangle then the sum of the measures of its interior angles is 180 degrees.

6

How many statements are normally needed to prove triangles congruent? (Sometimes you only need 3)