Angle-Side-Angle ASA Congruence If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Angle-Angle-Side AAS Congruence If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Hypotenuse-Leg HL Congruence right triangle If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent.
Angle-Angle AA Similarity If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. SSS for Similarity If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.
SAS for Similarity If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. Side Proportionality If two triangles are similar , the corresponding sides are in proportion.
Mid-segment Theorem also called mid-line The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. Sum of Two Sides The sum of the lengths of any two sides of a triangle must be greater than the third side.
Corresponding Angles If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding Angles Converse If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. Alternate Interior Angles If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Alternate Exterior Angles If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Interiors on Same Side If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. Alternate Interior Angles Converse If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
Alternate Exterior Angles Converse If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. Interiors on Same Side Converse If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel. In a circle, the perpendicular bisector of a chord passes through the center of the circle. A quantity is congruent equal to itself.
If equal quantities are added to equal quantities, the sums are equal. Subtraction Postulate. If equal quantities are subtracted from equal quantities, the differences are equal. If equal quantities are multiplied by equal quantities, the products are equal.
If equal quantities are divided by equal nonzero quantities, the quotients are equal. A quantity may be substituted for its equal in any expression.
The whole is equal to the sum of its parts. From a given point on or not on a line, one and only one perpendicular can be drawn to the line. If two angles form a linear pair, they are supplementary. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Base Angle Theorem Isosceles Triangle.
If two sides of a triangle are congruent, the angles opposite these sides are congruent. Base Angle Converse Isosceles Triangle. If two angles of a triangle are congruent, the sides opposite these angles are congruent. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Hypotenuse-Leg HL Congruence right triangle. If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. Corresponding parts of congruent triangles are congruent. No packages or subscriptions, pay only for the time you need. What is the exact meaning of these words in math : property , axiom , postulate , theorem , rule , law , principle.
Add comment. An axiom is a proposition regarded as self-evidently true without proof. Postulate is a true statement, which does not require to be proved.
More About Postulate Postulate is used to derive the other logical statements to solve a problem. Postulates are also called as axiom. A result that has been proved to be true using facts that were already known. Functions are usually represented by a function rul e where you express the dependent variable, y, in terms of the independent variable, x.
A pair of an input value and its corresponding output value is called an ordered pair and can be written as a, b. The theorem is not self evident. It is derived after considering the results of several logical statements often including other theorems. A famous example of this is the Pythagorean Theorem, which has nearly proofs.
Laws are statements which are inferred by observation. Laws are not proved. Through a point not on a line, one and only one parallel to that line can be drawn.
From a given point on or not on a line, one and only one perpendicular can be drawn to the line. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angles. If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. SA formula assumes a "closed box" with all 6 sides. Cube [special case of rectangular solid]. SA formula assumes a "closed container" with a top and a bottom. SA formula assumes a "closed container", with a bottom. Pyramid [assuming all of the faces not the base are the same]. NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.
Please read the " Terms of Use ". A quantity is equal to itself. Symmetric Property. Transitive Property. Addition Postulate. Subtraction Postulate. Multiplication Postulate.
Division Postulate. Substitution Postulate. Midpoint of Segment. Bisector of Segment. Euclid's Postulate 1. Euclid's Postulate 3. Any straight line segment can be extended indefinitely in a straight line. Straight Angles. Vertical Angles.
Triangle Sum.
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