# What are the 5 theorems of geometry?

## What are the 5 theorems of geometry?

In particular, he has been credited with proving the following five theorems: (1) a circle is bisected by any diameter; (2) the base angles of an isosceles triangle are equal; (3) the opposite (“vertical”) angles formed by the intersection of two lines are equal; (4) two triangles are congruent (of equal shape and size …

What theorems are there in geometry?

Theorem If a quadrilateral is a rectangle, then it is a parallelogram. Theorem If a parallelogram is a rectangle, then its diagonals are congruent. Theorem If a quadrilateral is a rhombus, then it is a parallelogram. If a parallelogram is a rhombus then its diagonals are perpendicular.

What are the theorems in lines and angles?

Theorem 6.1 : If two lines intersect each other, then the vertically opposite angles are equal. Proof : In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O as shown in Fig. 6.8.

### What are the 4 postulates in geometry?

Through any three noncollinear points, there is exactly one plane (Postulate 4). Through any two points, there is exactly one line (Postulate 3). If two points lie in a plane, then the line joining them lies in that plane (Postulate 5). If two planes intersect, then their intersection is a line (Postulate 6).

Is SS a similarity theorem?

SSS Similarity Theorem. By definition, two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. It is not necessary to check all angles and sides in order to tell if two triangles are similar. This is called the SSS Similarity Theorem.

What are all the postulates?

Euclid’s Postulates A straight line segment can be drawn joining any two points. Any straight line segment can be extended indefinitely in a straight line. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. All right angles are congruent .

#### What is the ASA theorem?

ASA Theorem (Angle-Side-Angle) The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles.

What are consecutive interior angles theorem?

Consecutive Interior Angles Theorem. Consecutive Interior Angles. When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.

What are the interior angles theorem?

The Same-Side Interior Angles Theorem states that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary. Supplementary angles are ones that have a sum of 180°.