Angle Pairs Complementary angles sum to 90 degrees. Consequently, I highly recommend that you keep a list of known definitions, properties, postulates, and theorems and have it with you as you work through these proofs. Study Flashcards On geometry postulates and theorems at Cram. Theorem 1. A postulate is a statement that is assumed true without proof. The vast majority are presented in the lessons themselves. Postulate 2: The measure of any line segment is a unique positive number.
Sides-Angles Theorem 2. Make sure that the angle is between the sides! Geometry postulates and theorems list with pictures pdf. Angle Bisector p36 5. Properties, properties, properties! A corollary is a statement that can be proved easily by applying a theorem. Some of the worksheets below are geometry postulates and theorems list with pictures ruler postulate angle addition postulate protractor postulate pythagorean theorem complementary angles supplementary angles congruent triangles legs of an isosceles triangle.
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Meta ironically urban dictionary saint-malo weather august RSS big enough is this short enough RSS soft things inside your bedroom. Division Postulate If equal quantities are divided by equal nonzero quantities, the quotients are equal. Substitution Postulate A quantity may be substituted for its equal in any expression. Partition Postulate The whole is equal to the sum of its parts.
Construction From a given point on or not on a line, one and only one perpendicular can be drawn to the line. Right Angles All right angles are congruent. Straight Angles All straight angles are congruent. Congruent Supplements Supplements of the same angle, or congruent angles, are congruent. Congruent Complements Complements of the same angle, or congruent angles, are congruent.
Linear Pair If two angles form a linear pair, they are supplementary. Vertical Angles Vertical angles are congruent. Exterior Angle The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle. 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.
Side-Side-Side SSS Congruence If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Side-Angle-Side SAS Congruence If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. 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. 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.
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