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Level 112

Congruence


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Side-Side-Side Congruence (SSS)
If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
Side-Angle-Side Congruence (SAS)
If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Angle-Side-Angle Congruence (ASA)
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Angle-Angle-Side Congruence (AAS)
If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Hypotenuse-Leg Congruence (HL)
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
CPCTC
Corresponding parts of congruent triangles are congruent.
Corresponding Parts
The parts (angles or sides) are in the same relative position in each of the figures
congruent figures
The SAME SIZE and SAME SHAPE
corresponding angles
Angles that have the same relative positions in geometric figures.
corresponding sides
Sides that have the same relative positions in geometric figures
Congruent Triangles
Triangles where all three angles and all three sides are congruent. The equal sides and angles may not be in the same position (if there is a reflection or rotation)
acute triangle
A triangle with three acute angles.
obtuse triangle
A triangle with one obtuse angle.
Right Triangle
A triangle with one right angle.
equiangular triangle
All angles of an acute triangle are equal.
Scalene Triangle
A triangle with no congruent sides
Isoceles triangle
At least two sides of a triangle are congruent.
equilateral triangle
Triangle with a 90° angle
Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180 degrees.
Third Angle Theorem
If two angles of a triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
Interior angle
angle on the inside of intersected parallel lines
Exterior angle
angle on the outside of intersected parallel lines
Remote Interior Angles
The measures of an exterior angle is equal to the measures of the two remote interior angles.
Acute angles
The _____________________________ of a right triangle are complementary.
Exterior angle theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Side-Side-Side Postulate
If the sides of one triangle is congruent to the sides of another triangle, then the triangles are congruent.
Side-Angle-Side Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another then the triangles are congruent.
Angle-Side-Angle Postulate
If two angles and the included side of a one triangle is congruent, then the triangles are congruent.
Angle-Angle-Side Postulate
If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side to a second triangle, then the two triangles are congruent.
Congruent
A plane figure with the same size and shape.