What are all the congruence theorems and postulates?

What are all the congruence theorems and postulates?

Congruent triangles are triangles with identical sides and angles. The three sides of one are exactly equal in measure to the three sides of another. The three angles of one are each the same angle as the other.

What are the 5 congruence postulates?

Thus the five theorems of congruent triangles are SSS, SAS, AAS, HL, and ASA.

  • SSS – side, side, and side.
  • SAS – side, angle, and side.
  • ASA – angle, side, and angle.
  • AAS – angle, angle, and side.
  • HL – hypotenuse and leg.

What are the 4 congruence theorems?

All right angles are congruent. All straight angles are congruent. Supplements of the same angle, or congruent angles, are congruent. Complements of the same angle, or congruent angles, are congruent.


Different rules of congruency are as follows. SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side)

What are the 4 postulates?

The four postulates presented by Darwin in On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life (eventually shortened to On the Origin of Species) are as follows: 1) Individuals within species are variable; 2) Some of these variations are passed on to …

What are the types of postulates?

Here are ten important geometry postulates that you absolutely need to know

  • Postulate 1.2.
  • Postulate 1.3.
  • Postulate 1.4.
  • Postulate 1.5 or ruler postulate.
  • Postulate 1.6 or segment addition postulate.
  • Postulate 1.7 or protractor postulate.
  • Postulate 1.8 or angle addition postulate.
  • Postulate 1.9.

What is 45 45 90 rule?

The main rule of 45-45-90 triangles is that it has one right angle and while the other two angles each measure 45° 45 ° .The lengths of the sides adjacent to the right triangle, the shorter sides have an equal length. Another rule is that the two sides of the triangle or legs of the triangle that form the right angle are congruent in length.

What are the 30 60 90 triangle rules?

What is the 30 60 90 triangle rule? In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.

What is the ratio of a 30 60 90 triangle?

The 30-60-90 triangle is called a special right triangle as the angles of this triangle are in a unique ratio of 1:2:3. Here, a right triangle means being any triangle that contains a 90° angle. A 30-60-90 triangle is a special right triangle that always has angles of measure 30°, 60°, and 90°. Here are some of the variants of a 30-60-90 triangle.

How to prove the SSS congruence theorem?

– SSS (side, side, side) SSS stands for “side, side, side” and means that we have two triangles with all three sides equal. – SAS (side, angle, side) – ASA (angle, side, angle) – AAS (angle, angle, side) – HL (hypotenuse, leg)