# Geometry Chapter 4, 5 Congruent Triangles

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Chapter 4 (McDougall Littell) Geometry terms, theorems, postulates, etc.

### Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

### congruent polygons

are congruent only if all corresponding parts are congruent

### corresponding part

the part of one shape has to be congruent to that same corner on the other shape

### SSS

If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent

### SAS

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent

### ASA

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

### AAS

If two angles and a NON-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent

### HL

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. *Only for use of right triangles

### Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then the point is an equal distance from the endpoints of the segment

### legs of isosceles triangle

are opposite base

### base of isosceles triangle

opposite two legs

### base angle of isosceles triangle

congruent angles on the base

### vertex angle

point at which the two legs meet (opposite base)

### Isosceles Triangle Theorem

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

### Converse of Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite the angle are congruent

### median of a triangle

a segment from a vertex to the midpoint of the opposite side

### altitude of a triangle

perpendicular segment from a vertex to the line that contains the opposite side

### SSA

Side-side-angle does NOT prove triangle congruence; exception is with a right triangle (see HL)

### CPCTC

Corresponding parts of congruent triangles are congruent; once two triangles have been proven congruent (by using SSS, SAS, ASA, AAS, or HL), then we can conclude its parts are congruent through CPCTC

### AAA

Angle-angle-angle does NOT prove triangle congruence (however, triangles will be similar; only need AA to prove similarity)

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